{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Introduction to Quantitative Finance\n",
    "\n",
    "Copyright (c) 2019 Python Charmers Pty Ltd, Australia, <https://pythoncharmers.com>. All rights reserved.\n",
    "\n",
    "<img src=\"img/python_charmers_logo.png\" width=\"300\" alt=\"Python Charmers Logo\">\n",
    "\n",
    "Published under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. See `LICENSE.md` for details.\n",
    "\n",
    "Sponsored by Tibra Global Services, <https://tibra.com>\n",
    "\n",
    "<img src=\"img/tibra_logo.png\" width=\"300\" alt=\"Tibra Logo\">\n",
    "\n",
    "\n",
    "## Module 2.4: Residual Analysis\n",
    "\n",
    "### 2.4.1 - Residual Analysis\n",
    "\n",
    "The residuals, or errors, are the difference between your predicted model and the actual values observed. Residuals are almost always there - natural variance causes random fluctuations, and our model may not incorporate all relevant information to analyse.\n",
    "\n",
    "Residuals can help you identify what changes to make to your model, and allow you to check your assumptions about the model are correct.\n",
    "\n",
    "In this module, we will revisit some of the concepts we have looked at in previous modules, but specifically with a focus on the residuals of a model. Previous notebooks generally looked at the data itself before the model is fit, rather than after.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Research \"Anscombe's Quartet\". What does it tell you about linear regression? How can residual analysis assist in finding issues caused by this type of problem?\n",
    "\n",
    "Note: In this notebook we will only use simple linear regression models, but the analysis techniques are applicable to any model.\n",
    "\n",
    "Let's start with a model that is accurate with regards to the data it is modelling:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%run setup.ipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 100)\n",
    "# y = 3x + 5 + e\n",
    "y_linear = x * 3 + 5 + np.random.random(len(x)) * 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f4614a63a0>]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_linear, 'bo', alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's now fit a linear model, and then review the residuals of this model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "X = sm.add_constant(x)\n",
    "model = sm.OLS(y_linear, X)\n",
    "results = model.fit()\n",
    "y_pred = results.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f462baa490>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_linear, 'bo', alpha=0.5)\n",
    "plt.plot(x, y_pred, 'r-', alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate the residuals\n",
    "e_linear = y_pred - y_linear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x1f462d45970>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Residual analysis - Linear\")\n",
    "plt.plot(x, e_linear, 'ro')\n",
    "plt.hlines(0, xmin=x.min(), xmax=x.max())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this plot, our linear model fits our linear data very well. As seen in the above plots, there is variability, but this residual plot, which plots the residuals against the x values, you can see a few very important components:\n",
    "\n",
    "1. The errors are centred around 0\n",
    "1. The errors look random, i.e. there are no trends\n",
    "1. The variability of the errors does not change\n",
    "\n",
    "We will now look at some examples of each of these three components not being seen.\n",
    "\n",
    "### Errors Centred Around 0\n",
    "It is a property of the linear regression model that errors will be centred around 0. In other words, regardless of your data, your residuals will be centred around zero. More formally, the expected value of the errors will be 0. For instance, here is a sine curve with a linear model fitted, and you can still see the errors are centred around zero:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f462c83ac0>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_sin = np.sin(x)\n",
    "plt.plot(x, y_sin)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f463e90eb0>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.OLS(y_sin, X)  # Capital X, which has constants already\n",
    "results = model.fit()\n",
    "y_pred = results.predict(X)\n",
    "\n",
    "e_sin = y_pred - y_sin\n",
    "plt.plot(x, e_sin, 'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a pattern here (we will come to that, but the residuals are still centred around zero. Due to this, the most common cause of your residuals not being centred around zero is actually a *coding* error, where some issue in the handling of your data has occurred or a computer bug.\n",
    "\n",
    "That said, if you forget to add a constant, it can happen too. Here we fit a linear model to our linear data, but forget the constant:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f462dbbd00>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = sm.OLS(y_linear, x)  # lowercase x, with no constant\n",
    "results = model.fit()\n",
    "y_pred = results.predict(x)\n",
    "\n",
    "e_linear_no_constant = y_pred - y_linear\n",
    "plt.plot(x, e_linear_no_constant, 'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here you can see the same spread of errors as our previous model, just not centred around zero. If you see errors not centred around zero, check for a constant, and then check your code for bugs! "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Write a function `fit_linear_plot_residuals` that takes the x and y values as input, fits a linear model, computes the residuals and then plots the residual plot. We will use this for the rest of our notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import statsmodels.api as sm\n",
    "def fit_linear_plot_residuals(x,y):\n",
    "    X = sm.add_constant(x)\n",
    "    model = sm.OLS(y, X)\n",
    "    results = model.fit()\n",
    "    y_pred = results.predict(X)\n",
    "    e_linear = y_pred - y\n",
    "    plt.title(\"Residual analysis - Linear\")\n",
    "    plt.plot(x, e_linear, 'ro')\n",
    "    plt.hlines(0, xmin=x.min(), xmax=x.max())   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/fit_linear_plot_residuals.py`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The next cell runs the solution, as it is needed. If you implemented your own (or improved it!)\n",
    "# then you can run your version here instead."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run -i solutions/fit_linear_plot_residuals.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_linear)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Errors must look random\n",
    "\n",
    "In addition to being centred around zero, errors must \"look random\". We have formal methods for this, but when doing statistical analysis, a good starting point is to plot the residuals and just eyeball the results. We saw in the linear examples above, the residuals are scatted around 0, with no clear patterns. Let's look at a counter example: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y = 3x**2 - 4x + 10 + e\n",
    "y_quad = 3 * x ** 2 - 4 * x + 10 + np.random.random(len(x)) * 90"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f463ea0ca0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_quad, 'bo')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_quad)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we can see a clear pattern in the residuals - there is an area of negative residuals, then an area of positive residuals and then another area of negative residuals. Whenever you can predict a residual based on the previous residual, you have a pattern. More formally, we want residuals to be iid - that is, independently and identically distributed.\n",
    "\n",
    "Note that other patterns may exist too - for instance, if the errors consistently \"flip\" between positive and negative, that is another pattern that should be accounted for.\n",
    "\n",
    "For example, the BDS test statistic tests for independence in a time series. It tests the following hypotheses:\n",
    "\n",
    "* $H_0$: The data is independent and identically distributed\n",
    "* $H_A$: The data has some autocorrelation\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "1. Using the `statsmodels.tsa.stattools.bds` function, test if the residuals above exhibit some autocorrelation.\n",
    "2. Using a different test from a previous notebook, test again for autocorrelation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Other patterns may be present in your data. For instance, seasonal trends are seen in many datasets, and this shows significantly in a residual plot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/residual_analysis_one.py`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y = sin(2{pi}x/12) + 3x + e\n",
    "# x is \"months\" since start\n",
    "x = np.linspace(0, 36)\n",
    "y_seasonal = np.sin(x * 2 * np.pi / 12) + (0.5 * x) + np.random.random(len(x)) * 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f463fbe880>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_seasonal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is a bit hard to see the seasonal trend, as it is masked by the strong linear trend and errors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_seasonal)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Even though the seasonal trend was present in the original data, it is more pronounced in the residual plot, which has the effect of demeaning, detrending and rescaling the data, showing patterns like this more clearly.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Investigate the `statsmodels.tsa.seasonal.seasonal_decompose` method for removing a known seasonal trend from data. Remove the \"seasonal\" trend from the data above (assume that the x value is \"number of months\") and fit a linear model to the non-seasonal data. Check the residuals of this fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The variability of the errors does not change\n",
    "\n",
    "A common issue that arises in datasets is that the variability of the errors changes with time (or increasing x for non-time series). This is a common occurrence in time series analysis. For example, as a stock price increases, a \"5% swing\" becomes a greater value. This is one reason to transform the data, but this pattern occurs in many other datasets. \n",
    "\n",
    "Let's have a look at some data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-10, 10, 100)\n",
    "\n",
    "# y = 3x + 5 + e*x\n",
    "y_variation = 3 * x + 5 + np.random.random(len(x)) * x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1f4640d4340>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_variation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiIAAAGdCAYAAAAvwBgXAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAAA16UlEQVR4nO3df5BU1Z338U8z4oAEZkVEBrp1CJvFzZKoi0bhcdTRrD+icZIp/AE+riZqrUYME61N/LFVgLUWaoxgaaLR8iHZUsAERmMeTRQ3M4JRU4hk10h0NQ46DLBIYmaI2QzSnOeP+9xxeqZ/3Nt9f9/3q2qq4fbt7ttze/p87znf8z0ZY4wRAABACEaFfQAAACC9CEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoDgr7AMo5cOCAduzYofHjxyuTyYR9OAAAwAFjjPbu3aupU6dq1KjyfR6RDkR27NihXC4X9mEAAIAq9PT0KJvNlt0n0oHI+PHjJVlvZMKECSEfDQAAcKK/v1+5XG6wHS8n0oGIPRwzYcIEAhEAAGLGSVoFyaoAACA0BCIAACA0BCIAACA0BCIAACA0BCIAACA0BCIAACA0BCIAACA0BCIAACA0kS5o5pt8Xtq4Udq5U2pslJqbpbq6sI8KAIDUSV8g0tEhLVokbd/+8bZsVrrnHqmtLbzjAgAghdI1NNPRIc2bVxiESFJvr7W9oyOc4wIAIKXSE4jk81ZPiDEj77O3tbdb+wEAgECkJxDZuHFkT8hQxkg9PdZ+AAAgEOkJRHbu9HY/AABQs/QEIo2N3u4HAABqlp5ApLnZmh2TyRS/P5ORcjlrPwAAEIj0BCJ1ddYUXWlkMGL/f8UK6okAABCg9AQiklUnZO1aadq0wu3ZrLWdOiIAAAQqfQXN2tqk1lYqqwIAEAHpC0QkK+g47bSwjwIAgNRL19AMAACIFAIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQGgIRAAAQmoPCPgAAAOCxfF7auFHauVNqbJSam6W6urCPqigCEQAAkqSjQ1q0SNq+/eNt2ax0zz1SW1t4x1UCQzMAACRFR4c0b15hECJJvb3W9o6OcI6rDAIRAACSIJ+3ekKMGXmfva293dovQghEAABIgo0bR/aEDGWM1NNj7RchBCIAACTBzp3e7hcQAhEAAJKgsdHb/QJCIAIAQBI0N1uzYzKZ4vdnMlIuZ+0XIQQiAAAkQV2dNUVXGhmM2P9fsSJy9UQCC0SWLVumTCaj9vb2oF4SAIB0aWuT1q6Vpk0r3J7NWtsjWEckkIJmmzZt0oMPPqjPfvazQbxcMsSoKh4AIELa2qTW1ti0Ib4HIn/60590ySWX6KGHHtK//uu/+v1yyRCzqngAgIipq5NOOy3so3DE96GZa6+9Vueee64+//nPV9x3YGBA/f39BT+pE8OqeAAAVMvXQGTNmjV69dVXtWzZMkf7L1u2TA0NDYM/uVzOz8OLnphWxQMAoFq+BSI9PT1atGiRHnnkEY0ZM8bRY2666Sb19fUN/vT09Ph1eNEU06p4AABUy7cckc2bN2v37t2aPXv24LZ8Pq8NGzbovvvu08DAgOqGJc7U19ervr7er0OKvphWxQMAoFq+BSJnnHGGXnvttYJtX/nKV3T00UfrW9/61oggBIptVTwAAKrlWyAyfvx4zZo1q2DbuHHjdNhhh43Yjv/ProrX21s8TySTse6PWFU8AACqRWXVKIlpVTwAAKqVMabYpXc09Pf3q6GhQX19fZowYULYhxOcYnVEcjkrCKGOCAAg4ty034FUVoVLMauKBwBAtQhEoipGVfEAAKgWOSIAACA0BCIAACA0BCIAACA0BCIAACA0BCIAACA0BCIAACA0BCIAACA01BEBACAK8vlUFrIkEAEAIGzFlvbIZq31xxK+tAdDMwAAhKmjQ5o3rzAIkayV2OfNs+5PMAKRNMrnpa4uafVq6zafD/uIACCd8nmrJ6TY+rP2tvb2RH9PE4ikTUeH1NQktbRICxZYt01NiY+4ASCSNm4c2RMylDFST4+1X0IRiKRJyrv/ACBydu70dr8YIhBJC7r/ACB6Ghu93S+GCETSgu4/AIie5mZrdkwmU/z+TEbK5az9EopAJC3o/gOA6Kmrs6boSiODEfv/K1Ykup4IgUha0P0HANHU1iatXStNm1a4PZu1tie8jkjGmGJJA9HQ39+vhoYG9fX1acKECWEfTrzl89bsmN7e4nkimYz1oe/uTnTkDQCRlaDKqm7abyqrpoXd/TdvnhV0DA1GUtL9BwCRVlcnnXZa2EcROIZm0iTl3X8AgOihRyRt2tqk1tbEdP8BAOKNQCSNUtr9BwCIHgKRKEhQghIAAG4QiIQtxUs/AwBAsmqYWPsFAJByBCJhYe0XAAAIRELD2i8AABCIhIa1XwAAIBAJDWu/AADArJnQ2Es/V1r7xc3Sz0wDBgDEDD0iYfF66eeODmtRu5YWacEC67apiZk3AIBIIxAJk1drvzANGAAQUxljio0LRIObZYRjrZYhlXze6vkoNQPHHuLp7maYBgAQCDftNzkiUVDL2i9upgGzvgwABIOcPccIROKOacAAEC0s3eEKOSJxxzRgAIgOcvZcIxCJO3sa8PCZN7ZMRsrl3E0DBgC4x9IdVSEQiTuvpwEDAKrD0h1VIRBJAq+mAYcln5e6uqTVq61brhYAxBE5e1UhWTUp2tqk1tb4ZWmT1AUgKcjZqwp1RBAeO6lr+EfQHlKKQ28OANjsuk6Vlu5IQV0nN+03QzMIB0ldAJKGnL2qEIggHCR1AUiiUjl706ZJS5ZIAwPkwg1DjgjCQVIXgKQanrP31lvSQw9Jixd/vA+5cIPoEUE4SOoCkGT20h319VZPCAXOSiIQQTgoxAYg6ciFc4RABOEgqQtA0pEL5wiBCMIT90JsAFAOuXCOkKyKcMW1EBsAVEIunCMEIgifndQFIDnyeS4w7Fy4SgXOUp4Lx9AMAMBbHR1WhdGWFmnBAuu2qSl9M0TIhXOEQAQA4B176YakTFetdVFOcuEqYq0ZAIA37LVWSs0UidtaK14uypmyoSo37Tc5IgAAb7iZrhr1vLBSi3LaPTtuezPIhSuJoRkAgDeSMl2VQmSBIhABAHgjKdNV41aIrNY8lpARiAAAvJGUpRvi1LOTgBlKBCIAAG8kZbpqXHp2EjJDiUAEAOCdJExXjUPPToLyWJg147eUTdkCgNgv3WD37MybZwUdQxv7qPTsJGiGEoGIn7ycgw4AcRL36ap2z06x7/AVK8L/Do9THksFvg7NLFu2TCeccILGjx+vyZMn60tf+pLefPNNP18yOhIydgcAqdXWJm3bJnV2SqtWWbfd3eEHIVJ88lgc8LWy6tlnn62LL75YJ5xwgvbv369bbrlFr732mrZu3apx48ZVfHxsK6smrbogACBa7Ham0oJ6IbUzkams+vOf/7zg/ytXrtTkyZO1efNmnXLKKX6+dLgSNHYHAIigOOSxOBTorJm+vj5J0sSJE4vePzAwoP7+/oKfWErQ2B0AIKKSMENJASarGmN0/fXX6+STT9asWbOK7rNs2TItXbo0qEPyT4LG7gAAERb3GUoKcPXda6+9Vk899ZReeOEFZbPZovsMDAxoYGBg8P/9/f3K5XLxzRGJ6NgdAAB+lpdwkyMSyNDMddddpyeffFKdnZ0lgxBJqq+v14QJEwp+Yikp1QUBAMkUodLwvgYixhgtXLhQHR0d+sUvfqHp06f7+XLRkpCxOwBAwkSsvISvQzNf+9rXtGrVKv3kJz/RzJkzB7c3NDRo7NixFR8f2+m7Q1FZFQAQFQGVl3DTfvsaiGRK1OlfuXKlLr/88oqPT0QgAgBAVHR1WcMwlXR21lReIjJ1RALKgwVKo0cKcIe/mWSLYHkJ1ppBcrHWD+AOfzPJF8HyEoEWNAMCE7FkLCDy+JtJh+ZmK7gskTqhTEbK5az9AkIgguTJ562rumJDg/a29nZrPwD8zaRJBMtLEIggedys9QOAv5m0iVh5CXJEkDwRTMYCIo2/mfSJUGl4AhEkTwSTsYBI428mnerqIrECPEMzSJ4oJWPl89a8/dWrrVvG2BFFUfqbQeoQiCB5opKMFaG1HICyovI3g1QiEEEyhZ2MxVRIxE3YfzNILV9LvNeKEu+omZ9VIks9d0BrOQC+oLIqPBCZEu9A6PxKxipXgXLiROdTISOQKAYUiEgCI9KDoRnArUrDLj/5ibPnYSokABCIAK44qUD56KPOnoupkADA0AzgipMKlO+/Lx1+uLRnT/GAxc4RYSokgEpSkLNDjwjghtPhlEsusW6ZCgmgWikpAUAgArjhdDiltZWpkACql6ISAEzfTboUdOsFyp6a29tbftjFnprL7x+AWwkoAcD0XVjKTTFNwhV5GI28XYFy3jzry2BoMFJs2IWpkID3kh7gu1kNOQHfLwzNJFXSu/XCHDulAiUQnjTkTaRsNWSGZpIoAd16Za947CBr+EfX7pEIKhhI+lUZEDVR+dv3W1eXFWBV0tkZ2R4RN+03gUgSRelDXE1jXW5IqbU1/kEWAPeScIHllNtctAhy034zNJNEUenWq6YLtdKQ0m23OR87BZAcbvIm4i5lqyETiCSR0ymmflb2rCZHxUnVUvuPs5KEjJ0CjuTzVk/o6tXWbT4f9hF5LyoXWEFJUS4as2aSqLnZ+rBW6tbzq7JnpYAik5Ha261hlqERvZMrnj/8wdkxUD4daZH02XG2KFxgBa2tzfqeTHguGj0iSRR2t161XahOr2QmThz5vmyZjJTLUT4d6ZD02XFD2RdYafvbt0sAzJ9v3SYsCJEIRJIrzG69artQnV7JLFpk3aZg7BQoyclQZnt7coZpwr7Agm8IRJKsrU3ats2aHbNqlXXb3e1/d221XahOr3huuSU1Y6dASV4kb8YttyRFeRNpQo5I0oVR2bPaHBU3VUuDHjulZgiiptbkzbjmlqQkbyJNCETgPbdl0Ieyr3iKfUGuWFH4BRlUkBXXL2wkWy3Jm6UKg9m5JVHvXWDphEShoBn8U6wBz+VGBhTFRKUHIi2VHBE/1Ra98qMwWFT+XhEZVFZFdMT5CypNlRwRT3agLBXveSwWKHtdeZkeQxRBZVVER5ynnqWpkiPiqZrkTS8Lg6Vp+jB8Q44IUEraKjkintwmb3pVGKzawoX4WJx7jD1EIAKUksZKjognN8mbXlVedtNjSGLpSAxpDWJoBiglrZUckWxeFQajx7B6DGkVIBCBM3ErfOQFKjkiqbwoDEaPYXXSVhHXAWbNoLK0dyHWMg0ZiLJachTcTh8mH8Li9ayliHLTfpMjgvLiXvjIC1RyRDXi0PDWUhjMTeHCtF/MDMWQ1ggMzaA0uhA/FudpyAheR4fVW9DSIi1YYN02NSVv7N/JEA/5EIUY0hqBoRmUlpIuxESLw1V50qSxGm+pzxlFAUeqtiJuzFDQDN6gCzHe0nJVHhX5vPTv/y5ddVX6ehFL9RhSFHAkkuBHIBBBaXQhxhfd4cGyg77Pf176wx9K75e2hpeLmeK8mLWUICSrojSvCh8hWFS8DFapoZhy0tLwcjFTGknwg+gRQWl0IcYT3eHBKRf0lZOWhpeigOWRBC+JQASV0IUYP3SHB6dS0Ddc2hpeLmbgAEMzqIwuxHihOzw4boI5pw1v0mY62RczxeqIUBQQYvoukDwpmR5YkZMGvdZG3+kUd8lZNd4kF/5KWoCFsty03wQiQBLZCZRS8YqXSR9Wc9Kge9HoVwr6JGniROlHP6qcA5DG+iNILAIRAKUb2quukj71qeRelTpp0CXvGn0vgj4KfyFhCEQAWIZ2h7/1lvTQQ8ns9rc5adDtxGsvG/1aF0akijEShsqqACz29MD6emnJkuoLnOXzVmO5erV1G9XKoE6mLm/f7v305rY2ads2K1BYtcq67e52HuAx0wkpxqwZIOlqLXAWpwRKLxtqt89Vy0q2zHRCitEjAiRdLQXO4lYq3suGOshGn8JfSDECESDpqu32r9STIkVvATcnDXo2G71Gn8JfSDECESDpqu32j2OpeCcN+j33RLPRL1XFeNo0K79nYCDa+TlAlQhEgKSrtts/rgmUTpYliOrSBcOTXpcutbYvXiwtWGDNrGlqit6QGFADpu8CaVBNrYu4TykNorKqnyhwhhijjgiAkdzWuqBUfHgocIaYc9N+M30XSAu3ixfa+Rbz5lkNX7GelKByKaLcc+EHN/k5UeyNAlwgEAHSxG2tiyisnBp2HZMwgqC45ucAVSAQAVCe256UWg0vS79kycihIbuOid95EmEFQRQ4Q4qQIwLEgZ9X5VEa9ijW8Jfid55EmMmi5Ocg5lhrBkiSjg6rUWpp8X4Kp5/PXc2xFKviWoqfdUzCLuZGgbNgxGUNpYQjEAGizM8S61Eq316u4a/EjzyJKBRzi2qtk6SIUhCecoEEIt/73vc0ffp0jRkzRrNnz9bGKFViBKLKz6vyWp/b6yvJSg1/OX7kSUQlWbTWVX1RXJSCcPgfiDz22GNqb2/XLbfcoi1btqi5uVnnnHOO3nvvPb9fGog3P6/Ka10Ir9oryVIBTDUN+vCKsF4GR1FKFrVnOs2fb90yHFMd+/Px6KPS1VfHaw2lhPN91szdd9+tK664QldeeaUkacWKFXrmmWd0//33a9myZX6/fFl/3rc/1NcHytq+Uxpd72w/t5/lap/7J09K//sS6wt76ON375HmXyI98qjUen7x5/rJk9I//7O0o/fjbVOnSd/+tnT4FGfHY7PzJL6zQsobKwgq9dyljqecE+dIR31S2rmjdLLo1GnWfnyPRF+xz165z9uu3VLnBumUdKx2fMjB4U6g9XXWzL59+3TIIYfoxz/+sb785S8Pbl+0aJF+/etf6/nnny/Yf2BgQAMDA4P/7+/vVy6X823WTNONT3n+nAAAxMm228/1/DkjM2tmz549yufzOuKIIwq2H3HEEdq1a9eI/ZctW6aGhobBn1wu5+fhAQCAkAXSH5MZNv3MGDNimyTddNNNuv766wf/b/eI+GXrrWf59tyAJ+yhEKl4ifVHHrVu7eGSoYbuU2x4wslzD33cj34sffUrlY/5/6yU6utHdoVXa1pWuvPO4u9hw0bpC+dUfo6nf2Z1s+fz0i9flHbtkqZMkf7X3Mo5F9U8BtHg9PMxlD3stvV1znNAfA1EJk2apLq6uhG9H7t37x7RSyJJ9fX1qq93MU5co7DHxYCKLmiT6h4tvVhda6uVKLrvL8Ufn8lIN7RLba0jv1RLPXc2K111lbR/QHrxhY8LnGUbpY8GVNE7JaqhunH44dLy5dbU1XIF1t7f5eyY3t8l/d8nq6ySepD0+WGrEEepCBxKc/r5sA3mHt0pjQ2uLUo947PPfe5z5pprrinY9rd/+7fmxhtvrPjYvr4+I8n09fX5dXhAPOzfb0xnpzGrVlm3+/db2zs7jbGa/PI/nZ3OnnvpUmOy2cLHZrPGrFtn7ZfNGpPJFH+NTMa6f/jjq/0pd8w2p+9/6dLix53JWD/r1jk/F+vWlf4dIVqcfj7sn1yO8+gRN+2374HImjVrzOjRo83DDz9stm7datrb2824cePMtm3bKj6WQASoYNUqZ1+wq1ZVfq516yo31vY+w/ez/3/55d4EIU6P2YvgKJOxGiA7uKv1d4ToqPT5kIw5/HBjHnmkMMBHzdy0377XEbnooou0YsUK3XrrrTr22GO1YcMGPf300zrqqKP8fmkg+byqd+G0wFlra/FqnxMnSocdJv3gB86Oxwkn781JKfSrrvKmHkvYZd/hXqXPRyYjPfCAdMkl1GgJEYveAXHm1eJoXV1WYbJKOjutL2wnK+RWq5oF3Yotlmfn0QwMWIXXKlm1yioaVorb3xGio9znIy1VagPOa3LTfpOtCcSZfcU3b57VgBeb/eJkcTS3Jc3tap92IOQmCDn8cCswuOee2o55qLY2q7em2BdtV5ez56jUAxOVsu9OkVD7sXKfjzQoFog5StQOiO8DRTUgRwRwqFgCpZvEu2qTXt0kAw7Po6jlmEsl75bat1IeiZMcES8Sg4NCQi1sIeU1uWm/GZoBkqKWK+Bqh3hWr3Y27CEV7wqv5pirubqzFzmTivfAOFnN1qthML/Z73X4Mbp5r0gG+zNbKkfKx8+sq/bbl1DII/SIAAEqNyOm1JWT016C5cu9mZFQy9Vdrb1GQ1/fze8oSHbvjxczhBB/IfbiRWrWDICYaGsrPiMmmy19Fd3cbN1fpFKypI9XyL3uutqvuGqdtdLWJm3bZiWTrlpl3XZ3u+sdqOZ3FCQ/V2xG/MQkr4lkVQAfc5vU51WyrBNuGtlSs1bsJNtaRDnxMSYNDwLi1fR+nxGIACjktrG2ewmK5W14OT0ySo2sFwGNH2LS8CAgdo9lpbym5ubgj20IApG4YCoeoiyIXgIa2cpi0vAgIEH2WNaAHJE46OiwMp9bWqwZCi0t1v87OsI+MuBjdi/B/Pn+VKl0mo+S5kbWSaXZCDQ8CFDU85pEIBJ99lS84WPjvb3WdoIRpAWNrDMxaHgQMC8StX1EHZEoC3EOOELEMFx5lOt2hs8RQuSm/SYQiTLWtkifqJdijgoaWSDSWGsmKaI0SwD+K1UR0x6GG9qtnvaGOKqzVgC4Ro5IlCVxlkA+b/X0rF5t3bJkusVNsS6SlwEkCIFIlCVtlgANaGlOi3XddhvJy3FGIA6MQCASZUmaJcDsn/KcDq/dc0/1Jc4RLgJxoCgCkahLwlS8WtcICVoYV61Oh9f+8IfS97GOSHQRiAMlMWsmLuKcnOjF7J+g3n9Ys1acLDF/6KHlAxHbqlVWUTFEA9Pw3Ynzdx0GuWm/6RGpRZBXzn5XrfRTrbN/gurSDvOq1ckw3KJFzp4rTsnLacCKuM4xfJVKBCLV4g/GuVpm/7gJDmoJDKMwfFRpGO6WW5KVvBxVXl9gMA3fGYav0stEWF9fn5Fk+vr6wj6UQuvWGZPJGGM1UR//ZDLWz7p1YR9htOzfb0w2W/x3Zv/ecjlrv2KPK/aY4Y9bt27kvtms83PR2Vn6dYb+dHZ6/dsZaf9+63VWrbJuh/5e7M/e8N8lnz1v1Po5KiZKn62ocvO3jlhw034TiLjFH0x1qmlAnX6BL11ae2C4apWz11q1yvNfjWvFGstcjiCkVn5dYFQbiKcJwVriuGm/GZpxi/He6lQz+yfIKa1xKh4X8QWsYsnPobkkTcP3C8NXqUYg4hZ/MNVz24AGOaU1bsXj4py8HEV+X2AkYRq+n+J0IQDPsdaMW/zB1MbNGiF2cODFlNZKgaF91TpvnvW8Q1+Pq9bkC+ICo61Nam1lamoxTv7Ws9noXAjAU/SIuBW3K+c4C3pKa61XrZTvjq+gLjCG92RJfGYkhq/SLoCclapFMlnVGGYuBK1ccqYfiYDlZq24OcZisy2qeW74L4yEUj9m6MQdidiJwayZICTpDyYOjWOUp7Q6nW1BwxNtQX6OKAFQWhy+j1CRm/abEu+1SEIp4rBKmnut2PvI5azu3CBKs1cq33333dKFF44c/7a7nUlYjIYgPkeUfEcKuGm/CUTSzK5kmJTGMYzA0Ok6OocfLr3/fvH7aHiixe/PkRdrLwER56b9ZtZMWlWqm5DJWHUTWlvj0zi6mZHjFaezKEoFIVLh1FAanvD5/TmiBABQgFkzaUVhNm94OU2bhicdKAEAFCAQSSuuyrzhZDr34Yc7ey4annSgBABQgEAkrbgq84aT+gff/S4NDz5GzYxgUNcnNghE0oqrMu9UKoR2wQU0PChEyXd/dXRYM5NaWqQFC6zbpiZrOyKHWTNpZs+akYqXNK/0hZiE6cteqvT7CGuKMaKLvyHvJW02YEwxfRfOVds4JqX+SNCKNTwSjRHgBWq0RAaBCNxxe1XGFYd3COgA71CjJTKoIwJ33NRNSGL9kbCUCuh6e63tBHSAO8wGjCWSVeEO9Ue8USmgk6yAjkx/wDlmA8YSgQjc4YrDGwR0gPeYDRhLBCJwhysObxDQAd6jRkssEYiUQjGc4rji8AYBHeAParTEDrNmimEmQ3m11h/Bx9MMe3uL54kwzRCoDTVaQuWm/aZHZDi7kR0+fm/PZKAyH1ccXqALGfCXPRtw/nzrlr+lyKJHZCiK4bgz/Ipj7lzpxRe5AnGDaqsAEog6ItVyM5OBYjiF9Uc6OqQZMxjOcqutzaq5QhcygJQiEBkqqJkMSRu7pDBXbdwUlAOAhCFHZKggZjIkbVVICnMBAGpAIDKU31NTk5gIS2EuAEANCESG8nMmQ1J7DijMBQCoAYHIcH5NTU1qzwGFuYD0oeAjPESyajF+zGSIW8+B04RaezirUmEuKq0CyUDBR3iMQKSUamcylGrA49Rz4OaLxh7OmjfPCjqKVVqlMBeQDMyQgw8YmvFSuRkxcVmjpZqEWiqtAsmX1Dw3hI7Kql4pdaUwdP0VKdprtNRaWTZp9VEAfKyry7q4qqSzk7o4oLJq4CpdKWQy1pVCd7cVbBQb9ohCSe9aK8tSmAsIRhhBf9zy3BAbBCJecNOAR7mkN180QPTVkixaSwATpzw3xAqBiBfcNuBR7TngiwaItlqSRWud7cIMOfiEZFUvJKUBj0tCLZBGtSSLelHV2c+Cj0g1AhEvJKUB54sGiK5qiyJ6OduFGXLwAYGIF5LUgKfxi4YqkYiDanO4vK7q3NYmbdtmzY5Ztcq67e5O5ncDAkGOiFfsBjyqM2LciHJCrdeoEom4qHYI2I8k9KjmuSGWqCPiNWppRNvQ8/PWW9KSJeVrvxCMICrsOj+VkkWH1/mh/gdC4Kb99m1oZtu2bbriiis0ffp0jR07VjNmzNDixYu1b98+v14yGuwrhfnzrVuCkOgYXvl28WKqRCI+qh0CTkoOGxLLt0DkjTfe0IEDB/T9739fr7/+upYvX64HHnhAN998s18vCZRWatZAKXFdDRnJVk0OV5Jy2JBIgQ7NfPvb39b999+vd955x9H+sRyaQfRUKl1fzqpVVu8WECXVDAEXy4fK5eKXw4ZYiGyJ976+Pk2cOLHk/QMDAxoYGBj8f39/fxCHhaSrNGugnKjXfkE6VZMsmqYkdMRKYIHI7373O9177736zne+U3KfZcuWaenSpUEdEtKimpL0VIlEEjHbBRHkOkdkyZIlymQyZX9eeeWVgsfs2LFDZ599ti644AJdeeWVJZ/7pptuUl9f3+BPT0+P+3cEDOe2V4NxcwAIjOsckT179mjPnj1l92lqatKYMWMkWUFIS0uLTjzxRP3gBz/QqFHOYx9yROCJStMeh2PcHABq4muOyKRJkzRp0iRH+/b29qqlpUWzZ8/WypUrXQUhgGfsWQPz5lm9HUODEfv/S5dKn/oU4+YAEDDfckR27Nih0047TUceeaTuuusuvf/++4P3TZkyxa+XBYpLUuVbAEgQ3wKRZ599Vm+//bbefvttZbPZgvsiXMwVScasAQCIHEq8AwAAT0WixDsAAEAlBCIAACA0gVZWBQAg9lhl3VMEIk7xwQMAFFuzJ5u1SgQw+64qDM04MXz5+JYW6/8dHWEfGQAgKKVW8e7ttbbTJlSFWTOV2B+84b8muwx4qaW3ASAJ6A22VFrF216fqrs7nb+fYZg145V83uqCKxar2dva2639ACBp6A3+WKVVvI2Renqs/eAKgUg5fPAApBXDEIWcruJdzWrfKUcgUg4fPABpRG/wSE5X8Xa72jcIRMrigwcgjegNHqm52coBsfMDh8tkrJW7m5uDPa4EIBAphw8egDSiN3gkexVvaWSbYP9/xQoSVatAIFIOHzwAaURvcHH2Kt7TphVuz2aZQVkDpu86UayATS7H8vEAksmeqtrbWzxPJO1TVZnSXJGb9ptAxCk+eADSxJ41IxUGI9RQggNu2m9KvDtVVyeddlrYRwEAwbCHIYqVM6c3GB4iEAEAFNfWJrW20hsMXxGIAABKozcYPmPWDAAACA2BCAAACA2BCAAACA05IgCAcFAWASIQAQCEoVihyGzWqmbN1OBUYWgGABAsu1ja8IX1enut7R0d4RwXQkEgAgAITj5v9YQUK+ptb2tvt/ZDKhCIAACCs3HjyJ6QoYyRenqs/ZAKBCIAgODs3Ontfog9AhEAQHAaG73dD7FHIAIACE5zszU7xl7Fd7hMRsrlrP2QCgQiAIDg1NVZU3SlkcGI/f8VK9zVE8nnpa4uafVq65ZE11ghEAEABKutTVq7Vpo2rXB7Nmttd1NHpKNDamqSWlqkBQus26YmpgDHSMaYYnOooqG/v18NDQ3q6+vThAkTwj4cAICXaq2satcjGd6M2T0rboMaeMZN+00gAgCIn3ze6vkoNRU4k7F6WLq7KRsfAjftN0MzAID4oR5JYrDWTJyxYBSApCv1PUc9ksQgEIkrFowCkHTlvueoR5IYDM3EEQtGAUi6St9z779PPZKEIBCJGxaMApB0Tr7nbrhBWr7c+rdX9UgQCgKRuCFBC0DSOf2emzTJu3okCA05InFDghaApHPzPTd/vtTaSuJ+jBGIxA0JWgCSzu33XF2ddNppvh0O/MXQTNywYBSApON7LlUIROLGjwWjACBKwvqei8PieXE4RpcIROLIywWjACCKgv6ei8PieXE4xiqw1kycUVkVQNIF8T0Xh8Xz4nCMQ7DoHQAATsRh8bw4HOMwLHoHAIATcajNFIdjrAGBCAAgveJQmykOx1gDAhEAQHrFoTZTHI6xBgQiAID0ikPNkjgcYw0IRAAA6RWH2kxxOMYaEIgAANItDrWZ4nCMVWL6LgAAUjxqM8XhGOWu/WbROwAApHgsnheHY3SJoRkAABAaAhEAABAaAhEAABAackQAAKhFTBJIo4pABACAanV0SIsWFa4Fk81adT9iPKU2SAzNAABQjY4Oad68kQvS9fZa2zs6wjmumCEQAQDArXze6gkpVorL3tbebu2HsghEAABwa+PGkT0hQxkj9fRY+6EsAhEAANzaudPb/VKMZFWJjGcAgDuNjd7ul2KB9IgMDAzo2GOPVSaT0a9//esgXtK5jg6pqUlqaZEWLLBum5pIMgIAlNbcbM2OGb4ari2TkXI5az+UFUgg8s1vflNTp04N4qXcIeMZAFCNujpriq40Mhix/79iBb3rDvgeiPzsZz/Ts88+q7vuusvvl3KHjGcAQC3a2qS1a6Vp0wq3Z7PWduqIOOJrjsh///d/66qrrtITTzyhQw45xM+Xcs9NxnPCVjoEAHikrU1qbSXPsAa+BSLGGF1++eW6+uqrdfzxx2vbtm0VHzMwMKCBgYHB//f39/t1eGQ8AwC8UVfHBWsNXA/NLFmyRJlMpuzPK6+8onvvvVf9/f266aabHD/3smXL1NDQMPiTy+XcHp5zZDwDABC6jDHFkiRK27Nnj/bs2VN2n6amJl188cX66U9/qsyQJJ58Pq+6ujpdcskl+uEPfzjiccV6RHK5nPr6+jRhwgQ3h1lZPm/NjuntLZ4nkslY43zd3XSxAQDgQn9/vxoaGhy1364DEafee++9gqGVHTt26KyzztLatWt14oknKpvNVnwON2+kKvasGakwGLGDJ5KNAABwzU377VuOyJFHHlnw/0984hOSpBkzZjgKQgJhZzwXWzlxxQqCEAAAfEZlVTKeAQAITWCBSFNTk3waBaodGc8AAISCRe8AAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoCEQAAEBoIl3i3a7EOnTxPAAAEG12u+2konqkA5G9e/dKknK5XMhHAgAA3Nq7d68aGhrK7pMxkV0ARjpw4IB27Nih8ePHK5PJePrc/f39yuVy6unpqbhEcRzx/uIv6e8x6e9PSv575P3Fn1/v0RijvXv3aurUqRo1qnwWSKR7REaNGqVsNuvra0yYMCGxHzCJ95cESX+PSX9/UvLfI+8v/vx4j5V6QmwkqwIAgNAQiAAAgNCkNhCpr6/X4sWLVV9fH/ah+IL3F39Jf49Jf39S8t8j7y/+ovAeI52sCgAAki21PSIAACB8BCIAACA0BCIAACA0BCIAACA0iQ1EbrvtNs2dO1eHHHKI/uqv/qroPu+9956++MUvaty4cZo0aZK+/vWva9++fWWfd2BgQNddd50mTZqkcePG6fzzz9f27dt9eAfudHV1KZPJFP3ZtGlTycddfvnlI/Y/6aSTAjxy55qamkYc64033lj2McYYLVmyRFOnTtXYsWN12mmn6fXXXw/oiJ3btm2brrjiCk2fPl1jx47VjBkztHjx4oqfx6ifv+9973uaPn26xowZo9mzZ2vjxo1l93/++ec1e/ZsjRkzRp/85Cf1wAMPBHSk7i1btkwnnHCCxo8fr8mTJ+tLX/qS3nzzzbKPKfV3+sYbbwR01M4tWbJkxHFOmTKl7GPidP6KfZ9kMhlde+21RfePw7nbsGGDvvjFL2rq1KnKZDJ64oknCu6v9vtw3bp1+vSnP636+np9+tOf1uOPP+7pcSc2ENm3b58uuOACXXPNNUXvz+fzOvfcc/Xhhx/qhRde0Jo1a7Ru3TrdcMMNZZ+3vb1djz/+uNasWaMXXnhBf/rTn3Teeecpn8/78TYcmzt3rnbu3Fnwc+WVV6qpqUnHH3982ceeffbZBY97+umnAzpq92699daCY/2Xf/mXsvvfeeeduvvuu3Xfffdp06ZNmjJliv7hH/5hcB2jqHjjjTd04MABff/739frr7+u5cuX64EHHtDNN99c8bFRPX+PPfaY2tvbdcstt2jLli1qbm7WOeeco/fee6/o/t3d3frCF76g5uZmbdmyRTfffLO+/vWva926dQEfuTPPP/+8rr32Wr388stav3699u/frzPPPFMffvhhxce++eabBefsU5/6VABH7N7f/d3fFRzna6+9VnLfuJ2/TZs2Fby39evXS5IuuOCCso+L8rn78MMPdcwxx+i+++4ren8134cvvfSSLrroIl166aX6j//4D1166aW68MIL9atf/cq7AzcJt3LlStPQ0DBi+9NPP21GjRplent7B7etXr3a1NfXm76+vqLP9cc//tGMHj3arFmzZnBbb2+vGTVqlPn5z3/u+bHXYt++fWby5Mnm1ltvLbvfZZddZlpbW4M5qBodddRRZvny5Y73P3DggJkyZYq5/fbbB7f95S9/MQ0NDeaBBx7w4Qi9deedd5rp06eX3SfK5+9zn/ucufrqqwu2HX300ebGG28suv83v/lNc/TRRxds+6d/+idz0kkn+XaMXtq9e7eRZJ5//vmS+3R2dhpJ5oMPPgjuwKq0ePFic8wxxzjeP+7nb9GiRWbGjBnmwIEDRe+P07kzxhhJ5vHHHx/8f7XfhxdeeKE5++yzC7adddZZ5uKLL/bsWBPbI1LJSy+9pFmzZmnq1KmD28466ywNDAxo8+bNRR+zefNmffTRRzrzzDMHt02dOlWzZs3Siy++6Psxu/Hkk09qz549uvzyyyvu29XVpcmTJ+tv/uZvdNVVV2n37t3+H2CV7rjjDh122GE69thjddttt5Uduuju7tauXbsKzld9fb1OPfXUyJ2vYvr6+jRx4sSK+0Xx/O3bt0+bN28u+N1L0plnnlnyd//SSy+N2P+ss87SK6+8oo8++si3Y/VKX1+fJDk6Z8cdd5waGxt1xhlnqLOz0+9Dq9pbb72lqVOnavr06br44ov1zjvvlNw3zudv3759euSRR/TVr3614gKrcTl3w1X7fVjqvHr5HZraQGTXrl064ogjCrYdeuihOvjgg7Vr166Sjzn44IN16KGHFmw/4ogjSj4mLA8//LDOOuss5XK5svudc845evTRR/WLX/xC3/nOd7Rp0yadfvrpGhgYCOhInVu0aJHWrFmjzs5OLVy4UCtWrNDXvva1kvvb52T4eY7i+Rrud7/7ne69915dffXVZfeL6vnbs2eP8vm8q999sb/JI444Qvv379eePXt8O1YvGGN0/fXX6+STT9asWbNK7tfY2KgHH3xQ69atU0dHh2bOnKkzzjhDGzZsCPBonTnxxBP1b//2b3rmmWf00EMPadeuXZo7d65+//vfF90/zufviSee0B//+MeyF25xOnfFVPt9WOq8evkdGunVd4dbsmSJli5dWnafTZs2VcyJsBWLfI0xFSNiLx7jVDXvefv27XrmmWf0ox/9qOLzX3TRRYP/njVrlo4//ngdddRReuqpp9TW1lb9gTvk5v194xvfGNz22c9+VoceeqjmzZs32EtSyvBz4+f5Gq6a87djxw6dffbZuuCCC3TllVeWfWzY568St7/7YvsX2x41Cxcu1H/+53/qhRdeKLvfzJkzNXPmzMH/z5kzRz09Pbrrrrt0yimn+H2YrpxzzjmD//7MZz6jOXPmaMaMGfrhD3+o66+/vuhj4nr+Hn74YZ1zzjkFPeTDxenclVPN96Hf36GxCkQWLlyoiy++uOw+TU1Njp5rypQpI5JtPvjgA3300Ucjor+hj9m3b58++OCDgl6R3bt3a+7cuY5e161q3vPKlSt12GGH6fzzz3f9eo2NjTrqqKP01ltvuX5sNWo5p/bskLfffrtoIGJn+O/atUuNjY2D23fv3l3yHHvN7fvbsWOHWlpaNGfOHD344IOuXy/o81fKpEmTVFdXN+KqqdzvfsqUKUX3P+igg8oGmmG77rrr9OSTT2rDhg3KZrOuH3/SSSfpkUce8eHIvDVu3Dh95jOfKfnZiuv5e/fdd/Xcc8+po6PD9WPjcu6k6r8PS51XL79DYxWITJo0SZMmTfLkuebMmaPbbrtNO3fuHDwpzz77rOrr6zV79uyij5k9e7ZGjx6t9evX68ILL5Qk7dy5U7/5zW905513enJcw7l9z8YYrVy5Uv/4j/+o0aNHu3693//+9+rp6Sn4oPqplnO6ZcsWSSp5rNOnT9eUKVO0fv16HXfccZKsseDnn39ed9xxR3UH7JKb99fb26uWlhbNnj1bK1eu1KhR7kdOgz5/pRx88MGaPXu21q9fry9/+cuD29evX6/W1taij5kzZ45++tOfFmx79tlndfzxx1f1WfabMUbXXXedHn/8cXV1dWn69OlVPc+WLVtCP19ODAwM6Le//a2am5uL3h+382dbuXKlJk+erHPPPdf1Y+Ny7qTqvw/nzJmj9evXF/RIP/vss95efHuW9hox7777rtmyZYtZunSp+cQnPmG2bNlitmzZYvbu3WuMMWb//v1m1qxZ5owzzjCvvvqqee6550w2mzULFy4cfI7t27ebmTNnml/96leD266++mqTzWbNc889Z1599VVz+umnm2OOOcbs378/8PdYzHPPPWckma1btxa9f+bMmaajo8MYY8zevXvNDTfcYF588UXT3d1tOjs7zZw5c8y0adNMf39/kIdd0Ysvvmjuvvtus2XLFvPOO++Yxx57zEydOtWcf/75BfsNfX/GGHP77bebhoYG09HRYV577TUzf/5809jYGLn319vba/76r//anH766Wb79u1m586dgz9Dxen8rVmzxowePdo8/PDDZuvWraa9vd2MGzfObNu2zRhjzI033mguvfTSwf3feecdc8ghh5hvfOMbZuvWrebhhx82o0ePNmvXrg3rLZR1zTXXmIaGBtPV1VVwvv785z8P7jP8PS5fvtw8/vjj5r/+67/Mb37zG3PjjTcaSWbdunVhvIWybrjhBtPV1WXeeecd8/LLL5vzzjvPjB8/PjHnzxhj8vm8OfLII823vvWtEffF8dzt3bt3sK2TNPid+e677xpjnH0fXnrppQUz2375y1+auro6c/vtt5vf/va35vbbbzcHHXSQefnllz077sQGIpdddpmRNOKns7NzcJ93333XnHvuuWbs2LFm4sSJZuHCheYvf/nL4P3d3d0jHvM///M/ZuHChWbixIlm7Nix5rzzzjPvvfdegO+svPnz55u5c+eWvF+SWblypTHGmD//+c/mzDPPNIcffrgZPXq0OfLII81ll10Wqfdj27x5sznxxBNNQ0ODGTNmjJk5c6ZZvHix+fDDDwv2G/r+jLGmrC1evNhMmTLF1NfXm1NOOcW89tprAR99ZStXriz6eR1+rRC38/fd737XHHXUUebggw82f//3f18wtfWyyy4zp556asH+XV1d5rjjjjMHH3ywaWpqMvfff3/AR+xcqfM19PM3/D3ecccdZsaMGWbMmDHm0EMPNSeffLJ56qmngj94By666CLT2NhoRo8ebaZOnWra2trM66+/Pnh/3M+fMcY888wzRpJ58803R9wXx3NnTzEe/nPZZZcZY5x9H5566qmD+9t+/OMfm5kzZ5rRo0ebo48+2vPgK2PM/88mAgAACFhqp+8CAIDwEYgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQEIgAAIDQ/D/u6KDA7J4/5gAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_variation)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It may be tempting in the first plot (`x` versus `y_variation`) to simply discard the \"random noise\" at the top and bottom, but the residual plot highlights quite clearly that the variation changes dramatically as x does. The data starts with a very high variability, moves to a very low variability and then again to a very high variability. \n",
    "\n",
    "Important: \"high\" and \"low\" are subjective, and relative to the general variability in the data. Do not apply a blanket rule like \"variability above 4 is bad\".\n",
    "\n",
    "This data is said to have violated the assumption of homoscedasticity for OLS. In cases of strong variability, the OLS estimator is still consistent, and generally works \"well enough\". It would be important to report that estimations in the areas of high variability would have less precision than predictions in areas of low variability. Weighted least squares could help as well.\n",
    "\n",
    "If you have control over the data itself, investigate what is causing the variability and look to remove it. For instance, if we are measuring a car's performance, the variability might be high in the morning with a cold-start of the engine. As it warms up, the engine performs more consistently. Remove this impact, or fit the data to the different \"cold start\" and \"warm start\" categories."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exercise\n",
    "\n",
    "Create a plot with variability increasing over time, and plot the residual graph."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#from solutions\n",
    "y_increasing = np.random.random(len(x)) * np.arange(len(x)) * 25  # Your equation may vary\n",
    "\n",
    "plt.plot(x, y_increasing, 'bo')\n",
    "\n",
    "fit_linear_plot_residuals(x, y_increasing)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/increasing_variability.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### QQ plots\n",
    "\n",
    "A common method of analysing residuals is to look at the QQ plot, the quantile-quantile plot. It plots the quantiles of the residuals against the quantiles of a normal distribution. If the residuals are normally distributed, this plot will show a straight diagonal line with random variability around that line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAksAAAGwCAYAAAC5ACFFAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAABlIElEQVR4nO3dd1yV5f/H8dcBWSriQAEVkRwlaubIVebInZY2Nbdmae5RaWZqpWaZWpnadGSZlVmaZm5Tc49yZQ4MU8gNiAoK9++P+8f5iqxz4MBhvJ+Px3l8ve9z3/f5IN/kzXVf9+eyGIZhICIiIiIpcnF2ASIiIiI5mcKSiIiISBoUlkRERETSoLAkIiIikgaFJREREZE0KCyJiIiIpEFhSURERCQNBZxdQF6QkJDA2bNn8fb2xmKxOLscERERsYFhGERHR1O6dGlcXFIfP1JYcoCzZ88SGBjo7DJEREQkA06fPk3ZsmVTfV9hyQG8vb0B8y+7SJEiTq5GREREbBEVFUVgYKD153hqFJYcIPHWW5EiRRSWREREcpn0ptBogreIiIhIGhSWRERERNKgsCQiIiKSBoUlERERkTTkqrD022+/0b59e0qXLo3FYuHHH39M8r5hGIwfP57SpUvj5eVFkyZNOHToULrXXbJkCSEhIXh4eBASEsLSpUuz6CsQERGR3CZXhaWYmBhq1KjBzJkzU3z/nXfeYdq0acycOZNdu3bh7+9PixYtiI6OTvWa27Zt45lnnqFbt2788ccfdOvWjaeffpodO3Zk1ZchIiIiuYjFMAzD2UVkhMViYenSpXTo0AEwR5VKly7N0KFDeeWVVwCIjY3Fz8+PKVOm8MILL6R4nWeeeYaoqCh++eUX677WrVtTrFgxFi1aZFMtUVFR+Pj4EBkZqdYBIiIiuYStP79z1chSWkJDQ4mIiKBly5bWfR4eHjRu3Jjff/891fO2bduW5ByAVq1apXlObGwsUVFRSV4iIiKSN+WZsBQREQGAn59fkv1+fn7W91I7z95zJk+ejI+Pj/WlpU5ERETyrjwTlhLd2YXTMIx0O3Pae87o0aOJjIy0vk6fPp3xgkVERCRHyzPLnfj7+wPmSFFAQIB1/7lz55KNHN153p2jSOmd4+HhgYeHRyYrFhERkdwgz4wsBQcH4+/vz5o1a6z74uLi2LRpEw0bNkz1vAYNGiQ5B2D16tVpniMiIiL5R64aWbp69SrHjx+3boeGhrJ//36KFy9OuXLlGDp0KJMmTaJSpUpUqlSJSZMmUbBgQZ599lnrOd27d6dMmTJMnjwZgCFDhvDQQw8xZcoUHnvsMX766SfWrl3Lli1bsv3rExEREQdISIBffoFHHnHI5XJVWNq9ezdNmza1bg8fPhyAHj16MG/ePF5++WWuX7/Oiy++yOXLl6lXrx6rV6/G29vbek5YWBguLv8bUGvYsCHffPMNr732GmPHjqVChQosXryYevXqZd8XJiIiIo7x77/QowesXw+LFkGnTpm+ZK7ts5STqM+SiIhIDvDtt/DCC3DlChQsCLNnQ/fuqR5u68/vXDWyJCIiIpJMVBQMHAhffmlu338/LFwIlSs75PJ5ZoK3iIiI5ENbtkCNGmZQcnGBsWNh61aHBSXQyJKIiIjkRjdvwvjx8Pbb5oTu4GAzMD3wgMM/SmFJREREcpejR6FrV9i929zu2RPefx+yaN6wbsOJiIhI7mAY8PHHUKuWGZSKFYPvvoO5c7MsKIFGlkRERCQ3OHcO+vSBn382tx9+GObPhzJlsvyjNbIkIiIiOduKFVC9uhmU3N1h2jRYvTpbghJoZElERERyqmvXYORIs18SQLVq8PXXZnDKRhpZEhERkZxnzx5zblJiUBo2DHbtyvagBApLIiIikpPEx8PkyVC/vvnUW+nSsGaNeevN09MpJek2nIiIiOQMp06Zy5Ns3mxuP/GE+fRbiRJOLUsjSyIiIuJchmEuT1KjhhmUCheGefPMtgBODkqgkSURERFxpsuX4cUX4ZtvzO2GDc1O3Hfd5dy6bqORJREREXGODRvg3nvNoOTqCm+8AZs25aigBBpZEhERkewWG2sueDt1qnkLrmJF+OorqFvX2ZWlSGFJREREss+hQ9ClC/zxh7ndt6/5pFvhws6tKw26DSciIiJZzzDgww+hTh0zKPn6wo8/wief5OigBBpZEhERkawWHg69esGvv5rbbdrAF1+Av79z67KRRpZEREQk6yxdanbd/vVXs6nkzJnmWm+5JCiBRpZEREQkK1y9CkOHwuefm9s1a5q9lEJCnFpWRmhkSURERBxr+3a47z4zKFks8Mor5r5cGJRAI0siIiLiKLduwcSJ8Oab5hpvgYFmg8nGjZ1dWaYoLImIiEjmnTgBXbuaI0gAzz4LH30ERYs6tSxH0G04ERERyTjDMJ9sq1HDDEo+PmaDya++yhNBCTSyJCIiIhl14QK88AL88IO53bgxzJ8PQUHOrcvBNLIkIiIi9lu92lzX7YcfwM0NpkyBdevyXFACjSyJiIiIPa5fh1Gj4IMPzO177jFvudWq5dy6spDCkoiIiNjmjz/Mdd0OHTK3Bw40R5QKFnRuXVlMt+FEREQkbQkJMHUq1K1rBiU/P1i50lzrLY8HJdDIkoiIiKTl9Gno0QM2bDC3H3sMPv0USpZ0bl3ZSCNLIiIikrJvvzUncW/YYI4gffKJudZbPgpKoJElERERuVNkJAwaZHbfBrj/fnMSd6VKzq3LSTSyJCIiIv+zebPZYPLLL8HFBcaOha1b821QgjwWlsqXL4/FYkn2GjBgQIrHb9y4McXj//rrr2yuXERExMni4mDMGGjSBP75B4KDzeD0xhtmH6V8LE/dhtu1axfx8fHW7YMHD9KiRQueeuqpNM87evQoRYoUsW6XzGf3YkVEJJ/76y9zXbc9e8ztXr1gxgy47WdjfpanwtKdIeftt9+mQoUKNE5nteNSpUpR1I71a2JjY4mNjbVuR0VF2VWniIhIjmAY8PHHMHy42WyyWDFzEveTTzq7shwlT92Gu11cXBwLFy6kd+/eWCyWNI+tWbMmAQEBPPzww2xIfDQyDZMnT8bHx8f6CgwMdFTZIiIi2eO//6B9e+jf3wxKzZvDgQMKSinIs2Hpxx9/5MqVK/Ts2TPVYwICAvjkk09YsmQJP/zwA3fffTcPP/wwv/32W5rXHj16NJGRkdbX6dOnHVy9iIhIFvr5Z6heHVasAA8PmD4dfv0VypRxdmU5ksUwDMPZRWSFVq1a4e7uzvLly+06r3379lgsFpYtW2bzOVFRUfj4+BAZGZlk7pOIiEiOEhMDI0fCnDnmdvXqZkuA6tWdW5eT2PrzO0+OLP3zzz+sXbuW5557zu5z69evz7Fjx7KgKhERESfavdtc7DYxKA0fDjt35tugZI88NcE70dy5cylVqhSPPPKI3efu27ePgICALKhKRETECeLjzcVux42DW7fMW23z58PDDzu7siwRn2CwM/QS56JvUMrbk7rBxXF1SXvucnryXFhKSEhg7ty59OjRgwIFkn55o0eP5syZMyxYsACAGTNmUL58eapWrWqdEL5kyRKWLFnijNJFREQc69Qp6NYNtmwxt5980nz6rXhxp5aVVVYdDGfC8sOER96w7gvw8WRc+xBaV8v4QEieC0tr164lLCyM3r17J3svPDycsLAw63ZcXBwjR47kzJkzeHl5UbVqVVasWEHbtm2zs2QRERHHMgxYuBAGDIDoaPD2hpkzzeCUzhPiudWqg+H0X7iXOydiR0TeoP/CvczuWivDgSnPTvDOTprgLSIiOcbly9Cvn7kILkDDhmZwCg52bl1ZKD7B4MEp65OMKN3OAvj7eLLllWZJbsnl6wneIiIi+dL69XDvvWZQcnWFN9+ETZvydFAC2Bl6KdWgBGAA4ZE32Bl6KUPXz3O34URERPKd2Fh47TV47z3zFlylSuZoUt26zq4sW5yLTj0oZeS4OyksiYiI5GaHDkGXLvDHH+b288/DtGlQqJBz67pNVjyhdrtS3p4OPe5OCksiIiK5UUKCOWn75ZfNkSVfX/j8c3j0UWdXlkRWPaF2u7rBxQnw8SQi8kayCd7wvzlLdYMz9hSg5iyJiIjkNmfPQtu2MGSIGZTatDHXdXNwUIpPMNh24iI/7T/DthMXiU+w75mwxCfU7pxPlPiE2qqD4Q6p09XFwrj2IYAZjG6XuD2ufUiGR7M0siQiIpKbLF0KffvCxYvg6WnOU+rf3+EtATI7IhSfYDBh+eEUR3oMzBAzYflhWoT4O+SWXOtqAczuWitZzf7qsyQiIpJPREfD0KHwxRfmds2a5rpuVao4/KMc0bPInifUGlQokfmiMQNTixB/dfAWERHJd7Zvh65d4cQJcwTplVdgwgRwd3f4RzlqRCirn1BLjauLxWHhK5HmLImIiORUt27B+PHw4INmUCpXDjZsgMmTsyQogeN6FmX1E2rZSSNLIiIiOdHx4+Zo0o4d5naXLubTb0WLZunHOmpEKKufUMtOGlkSERHJSQzDbAFw331mUPLxga+/NptMZnFQAseNCGX1E2rZSWFJREQkp7hwAR5/HJ57DmJiiKzbkNWLVrOtbssUH9u359F+W49NHBFKLcJYMJ+Ks2VEKPEJNX+fpMHK38czUwvbZjctpOsAWkhXREQy7ddfoWdPiIggoYAbs5r3ZFr1diS4uALJH9u359F+e9sAJD4NByS5hZYYoOwNOlndwTujbP35rbDkAApLIiKSYdevw6hR8MEHAFy9qxLPPDSQQ34Vkhx2e1ABUny0P6Uwk1obgPSCT3Z03nY2haVspLAkIiIZ8scf5sTtQ4cASBgwgGYl23DqesqHWwC/Ih6AhYiolCdYJ06c3vJKMwAenLI+1afbbj82pZGenDoi5Ci2/vzW03AiIiLZLSHBXOx2zBiIiwM/P5g7lx2V63Lq0+2pnmYAEVGxaV76zkf7M9MYMit6FuVGCksiIiLZ6fRp6NHD7JcE5npun30GJUtybv8Zh32MPc0eHd0YMq9RWBIREckuixdDv35w5QoULAgzZphPvv3/um6ObNBoz7VyQ2NIZ1JYEhERyWqRkTBwoNkrCaBuXfPPlSolOcyWRo6Jc5b+i7Kt2WNeaQzpTOqzJCIikpU2b4YaNcxw5OICY8cS/9tmtrkUT9bzyJZGjuMfrcr4R21r9piXGkM6k56GcwA9DSciIsnExZnrur39ttmVOzgYFi5kVZHgdB/Jt+Wx/azss5RfqHVANlJYEhHJv1J8vP7voxhdu2LZsweAc08+S4lPZ7Hm32s29zyy5bF9ex7tz+ttADJCYSkbKSyJiORPyUZsDIMX/1rDsF8/wS32Blc8CzO61UB+uedB/It4cONWAleu3UzxWun1PBLHU58lERGRLHRnZ2zfmMtM+eUDHj6xC4DNQfcx8pGh/OftC9jXH0m9jXIWhSUREREb3H4by7eQB+OXHbYGpWbHd/LOL+/jey2SWFc3pjTuydw67TEs9j9HpZ5HOY/CkoiIyG1Smtuz5nBEsgnSAF5xNxiz4XO67v8FgCMlyzO0/UiOliyf4c9Xz6OcR2FJRETk/6X01FjRgm4pzjOqHn6MGT9PpcIls+v2p/d3YOpD3Ykt4J6hz1bPo5xLYUlERITkc5AS3RmUXBLi6bdjCcO2fIVbQjzhhUsw4pFh/F7+vgx/tnoe5WwKSyIiku/FJxhMWH44xS7Xtyt7JYLpP0/j/jOHAVhx9wO82mogkV7eNn2OBfAp6IZnAVciov43euWvnkc5msKSiIjkeztDLyWbj5SEYdDx0AbeWDMb77jrRLt7Ma5FP36o2sy6rlt6Eo96+/HqtAjxV8+jXERhSURE8r20nkDzuR7NxNWzaPfXZgB2l6nC0HYj+Leof4rHB/h48miNAJb9EZ4kgN05eqT2ALmHwpKIiOR7qT2B1uCfP5j28zQCrl7kposrMx54ljn1nyTexRX438K27z19HxeuxiYZJXq5dRWNHuUReWoh3fHjx2OxWJK8/P1TTv6JNm3aRO3atfH09OSuu+5izpw52VStiIhkp/gEg20nLiZZvDZxX0TkdYoXcrfeKnO/dZNX13/Oom/GEHD1IieLleaJru/yUcNnkgQlMBe2faCiL4/dV4YGFUpYA5Gri4UGFUok2y+5T54bWapatSpr1661bru6uqZ6bGhoKG3btqVv374sXLiQrVu38uKLL1KyZEmeeOKJ7ChXRESyQWotASD5026Vz59ixs/vEXIuFICva7TmzWbP4VHUG247VpOy8488F5YKFCiQ7mhSojlz5lCuXDlmzJgBQJUqVdi9ezdTp05VWBIRySNsbQlgMRLouWc5ozbOwyP+Jhe9ivBKmyEcqtOY6e1DNCk7H8tzYenYsWOULl0aDw8P6tWrx6RJk7jrrrtSPHbbtm20bNkyyb5WrVrx+eefc/PmTdzc3FI8LzY2ltjY/63xExUV5bgvQEREHMbWlgCloi8ydeUMHjq1D4DNleoS/dEc+txVLkko0qTs/ClPzVmqV68eCxYs4Ndff+XTTz8lIiKChg0bcvHixRSPj4iIwM/PL8k+Pz8/bt26xYULF1L9nMmTJ+Pj42N9BQYGOvTrEBGRzEmcizR9zdG0WwIArY7+zq9fDOShU/u4UcCd11r0p1vHsRS7q5zmGgmQx0aW2rRpY/1z9erVadCgARUqVGD+/PkMHz48xXMsd/THMAwjxf23Gz16dJLrRUVFKTCJiOQQKc1PSkmh2GuMW/cJTx8w57ke8KvA0HYjOeFr/nuuBW0lUZ4KS3cqVKgQ1atX59ixYym+7+/vT0RERJJ9586do0CBApQokfpQq4eHBx4eHg6tVUREbJPSQrdgNpZccziCL7aeSvcatc4cYfrP7xF0JYIELHxc7wmmNerCTdf/Tb/QgraSKE+HpdjYWI4cOUKjRo1SfL9BgwYsX748yb7Vq1dTp06dVOcriYhI9ro9HJ26cI1FO8OSLBWS2lNtKXFNiGfQ798w8PfFFDAS+LdISYa3G8HOwGrWY7SgrdwpT4WlkSNH0r59e8qVK8e5c+d46623iIqKokePHoB5++zMmTMsWLAAgH79+jFz5kyGDx9O37592bZtG59//jmLFi1y5pchIiL/z5ZbaraEJICgy2eZsfw9aoYfBWBpSBPGtehHlGdh6zFa0FZSkqfC0r///kvnzp25cOECJUuWpH79+mzfvp2goCAAwsPDCQsLsx4fHBzMypUrGTZsGB999BGlS5fmgw8+UNsAEZEcILVH/u1mGDz95xrGrfuEQjdvEOVRiNdavshvdZqbTzmpd5Kkw2IkzmiWDIuKisLHx4fIyEiKFCni7HJERHK9+ASDB6esT3eSdnqKXYvk7VUf0urYdgC2B1bjj4kfcG/De5PMdVLvpPzJ1p/feWpkSURE8oadoZcyHZQeOrmHqStnUCrmMnEuBXjvoW783LwTv3VpkiQQqXeSpEdhSUREst3tk7Z9C3mABetCtLWDirH1eOq97tLjcTOWUZvm0WuP+QDPsRKBDGn/Ekf87mL2Y9U1ciR2U1gSEZEsl94TbbdzsUBCBieIhPx3khnLp1L5ojk/dV6tdkxu0ovivj7M1lwkySCFJRERyVK2NolMlJGgZDESeG7nj7z02wLcE25xrlAxXmo7lIrdnmBeiL/mIkmmKCyJiEiWiE8wmLn+ONPX/p2ln3P3zcu8uXQqdUP/AGB1pfpMf2okQzo31EiSOITCkoiIONyqg+GMX3aIiKjY9A+2k38RDzrXLUd530JU2bSSSuNfxnLlCvFeBTkwchze3Xvz811a000cR2FJREQcInFekq1LjmTEwKYVGNbiblyjo2DgQFi40Hyjbl1cFy7kvkqVsuRzJX9TWBIRkUyzd15SRj1QsSSuW7dAt27wzz/g4gKvvWa+tEyVZBGFJRERyRSHddpOgwUoW8iVep9NhSlTwDAgONgcWWrYMAs/WURhSURE7HR7G4DiXu68uvRglgeluy6e5odls3A5csDc2asXvP8+eHtn4SeLmBSWREQkXbfPR/px/1kuxcRl2Wcl6bNkGPT/aw0jVn+C640bULw4fPIJaA1PyUYKSyIiAqTeVTu9JpIZcfsTbSl18N7zz2UiT52m3sSXKbZhjXlS8+Ywbx6UKeOwOkRsobAkIiLZNkEbYFjzSgxsVinNR/sbHNkGvXvD+fPg4WHOUxo0yJzQLZLNFJZERPKx7GocCRDg48m49JYciYmBkSNhzhxzu3p1+Oor839FnERhSUQkn8rKxpG36/NAeZrbsuTI7t3QpQv8/f/BbdgwmDQJPD2ztD6R9CgsiYjkQ9nxuH+JQu5M7Fgt/SVH4uPN22zjxsGtW+acpPnz4eGHs7A6EdspLImI5DPxCQYTlh/O0qBUvJAb20Y/jHuBdOYYhYaaDSa3bjW3n3rKvAVXvHgWVidiH4UlEZF8IvFpty3HzmfZRO7Em2yTOlZPOygZhtlQcsAAiI42+yXNnGkGJ4vWdJOcRWFJRCQfyK6n3fxtmcR96RL07w/ffmtuP/AAfPml2ZFbJAdSWBIRycOy6mm34oXc6HhfGZrd45ekR1K6k7jXr4fu3eHMGShQwJynNGqU+WeRHEr/7xQRyaMc+bTb7U0kbQpFd4qNhTFj4L33zO3Klc3bcPffn+naRLKa3WFp7969uLm5Uf3/e1789NNPzJ07l5CQEMaPH4+7u7vDixQREds5YjRpyMMVqRtcwvYRo7QcPGi2BPjzT3P7hRfM0FSoUIbrE8lOdoelF154gVGjRlG9enVOnjxJp06d6NixI9999x3Xrl1jxowZWVCmiIik5fa125buO8PlazczdJ2iBd14+/Hq6T/ub4uEBPjwQ3jlFXNkydcXPv8cHn0089cWyUZ2h6W///6b++67D4DvvvuOhx56iK+//pqtW7fSqVMnhSURkWzmyMnbH3WuxQOVfDNf1Nmz0KsXrF5tbrdtawYlf//MX1skm9kdlgzDICEhAYC1a9fSrl07AAIDA7lw4YJjqxMRkTQ5qrmkBfNJtvoVSmS+qB9+gL59zafePD3NW279+6slgORadoelOnXq8NZbb9G8eXM2bdrE7NmzAQgNDcXPz8/hBYqISMribiXw6tKDDmsuOa59SMbnJYHZL2noUPjiC3O7Vi1zEneVKg6pT8RZ7F6+ecaMGezdu5eBAwcyZswYKlasCMD3339Pw4YNHV6giIgkt+pgOPUnr+VSTFymrxXg48nsrrUyN09p2za47z4zKFksZjuAbdsUlCRPsBiG4ZBfSm7cuIGrqytubm6OuFyuEhUVhY+PD5GRkRQpUsTZ5YhIHrfyz3Be/Hpvpq7xZK0yPFCpJP5FMvmk261b8NZb5is+HsqVMxtMPvRQpuoTyQ62/vzOUJ+lK1eu8P3333PixAleeuklihcvzuHDh/Hz86NMmTIZLlpERNK28s+zDFy0L8PnB9jSYdtWx49D166wY4e53bWruWSJj0/mry2Sg9gdlv78808efvhhihYtyqlTp+jbty/Fixdn6dKl/PPPPyxYsCAr6hQRydcc0TtpWPNKDGxWKXPzksBc1+3zz835STExZjiaPRs6d87cdUVyKLvnLA0fPpxevXpx7NgxPD09rfvbtGnDb7/95tDiRETEnJ/0wNvrMhyUAnw8mdO1FkOaV858ULpwAR5/3HzaLSYGmjQxm00qKEkeZvfI0q5du/j444+T7S9TpgwREREOKUpEREwZbQ1QxLMAT9UuS/MQ/8zNSbrdr79Cz54QEQFubjBxIowYAS52/94tkqvYHZY8PT2JiopKtv/o0aOULFnSIUWJiIh5623C8sN2B6XihdzYPro57gUcFGKuXzefbvvgA3O7ShX4+mvz6TeRfMDu/5Iee+wx3njjDW7eNFvpWywWwsLCGDVqFE888YTDC7TH5MmTuf/++/H29qZUqVJ06NCBo0ePpnnOxo0bsVgsyV5//fVXNlUtIpKynaGXMtSVe1LH6o4LSvv3Q506/wtKAwfCnj0KSpKv2P1f09SpUzl//jylSpXi+vXrNG7cmIoVK+Lt7c3EiROzokabbdq0iQEDBrB9+3bWrFnDrVu3aNmyJTExMemee/ToUcLDw62vSpUqZUPFIiKpOxdtX1ByscCsZzPZLylRQgK8+y7UrQuHD5vLlKxcaa715uWV+euL5CJ234YrUqQIW7ZsYf369ezdu5eEhARq1apF8+bNs6I+u6xatSrJ9ty5cylVqhR79uzhoXR6fpQqVYqiRYva9DmxsbHExsZat1O6LSkiklmlvD3TP+g2MzvXpO29DghKp09D9+6wcaO53aEDfPIJaKqF5FMZ6rME0KxZM5o1a+bIWhwuMjISgOLFi6d7bM2aNblx4wYhISG89tprNG3aNNVjJ0+ezIQJExxWp4hISuoGFyfAx5OIyBtpzltyaO+kxYuhXz+4cgUKFYL334fevbWum+RrNnXw/iDxXrUNBg8enKmCHMUwDB577DEuX77M5s2bUz3u6NGj/Pbbb9SuXZvY2Fi+/PJL5syZw8aNG1MdjUppZCkwMFAdvEXE4RKfhgNSDEwO650UGWnOR1q40NyuW9f8s6YkSB5mawdvm8JScHCwTR9qsVg4efKk7VVmoQEDBrBixQq2bNlC2bJl7Tq3ffv2WCwWli1bZtPxWu5ERLJCfILBztBLrDkcwY/7zyZZB86ho0mbN0O3bvDPP2YbgDFjYOxYsz2ASB7m0OVOQkNDHVZYdhg0aBDLli3jt99+szsoAdSvX5+Fib9diYg4waqD4UxYfjjJ03DFC7nR8b4yjuudFBcH48fD22+bXbnvusscTWrQIHPXFcljMjxnKScyDINBgwaxdOlSNm7caPOI2J327dtHQIADflsTEcmA1BbKvRxzky+2nuJ+RwSlv/4y13Lbs8fc7tnTbA/g7Z2564rkQTaFpeHDh/Pmm29SqFAhhg8fnuax06ZNc0hhGTFgwAC+/vprfvrpJ7y9va0dxX18fPD6/0ddR48ezZkzZ6xr2M2YMYPy5ctTtWpV4uLiWLhwIUuWLGHJkiVO+zpEJP9JvOX266Fw5m/7J8VjDMACTFh+mBYh/hkLTIYBc+aYnbevX4fixc0n3ZzcJ08kJ7MpLO3bt8/ahHLfvoyvdp3VZs+eDUCTJk2S7J87dy49e/YEIDw8nLCwMOt7cXFxjBw5kjNnzuDl5UXVqlVZsWIFbdu2za6yRSSfS+mWW2oMIDzyBjtDL9GgQgn7Pui//6BPH1ixwtxu0QLmzoUyZewvWiQfsWmCt6RNE7xFJKMyuvbb+53u47H77Ag5y5ebQen8efDwgClTYNAgresm+ZqtP7/t/q+kd+/eREdHJ9sfExND79697b2ciEi+ldG138COhpUxMWbfpEcfNYNS9eqwaxcMGaKgJGIju/9LmT9/PtevX0+2//r169Z5QCIikr6Mrv0W4ONJ3eD0m+2yezfUqgUff2xuDx8OO3eagUlEbGbz03BRUVEYhoFhGERHR+Pp+b/fauLj41m5ciWlSpXKkiJFRPIie9d+SzSufUjak7vj4812AOPHw61b5pykefMgByxLJZIb2RyWihYtisViwWKxULly5WTvWywWLQEiImIH38Iedh3vYoGZndNZKDc01GwwuXWruf3UU+bTbzYs+yQiKbM5LG3YsAHDMGjWrBlLlixJst6au7s7QUFBlC5dOkuKFBHJa1YdDGf8skN2nZPmQrmGAV9+aS5ZEh1t9kuaOdMMTlrXTSRTbA5LjRs3Bsxu3oGBgbhoYqCISIak1nQyNekubXLpEvTvD99+a24/+KAZnMqXz3yxImJ/B++goCCuXLnCzp07OXfuHAkJCUne7969u8OKExHJa1b+eZaBi9LvV2fz0ibr10P37nDmDBQoYM5TGjUKXF0dW7hIPmZ3WFq+fDldunQhJiYGb29vLLcN71osFoUlEZFUrDoYzotf29bY98NOtXigkm/qB8TGmgvevveeuV25srmu2/33O6BSEbmd3ffSRowYYe21dOXKFS5fvmx9Xbp0KStqFBHJ9RJ7KtnqQkxs6m8eOgR16/4vKL3wAuzdq6AkkkXsDktnzpxh8ODBFCxYMCvqERHJk7afvGhXT6UUm04mJMCMGVC7Nvz5J5QsCcuWmU+7FSrkuGJFJAm7w1KrVq3YvXt3VtQiIpInrToYzoCv7JvQnazp5Nmz0Lo1DBtm3oJr29YMTO3bO7haEbmT3XOWHnnkEV566SUOHz5M9erVcXNzS/L+o48+6rDiRERys/gEg5nrjzN97d92nZes6eSSJfD88+ZTb15e5u23fv3UEkAkm9i9kG5aLQMsFgvx8fGZLiq30UK6InKnxD5KEVFpzD26Q2LTSWsvpehocw23uXPN7Vq14Kuv4J57sqBikfzH1p/fdo8s3dkqQEREklp1MJz+C/favUBukqaT27ZB165w8qQ5gjRqlNkWwN3d0eWKSDrsDksiIpK6xKfe7AlKRQu68fbj1c2mkzdvwltvma+EBChXzmww+dBDWVaziKQtQ2EpJiaGTZs2ERYWRlxcXJL3Bg8e7JDCRERyk/gEg52hl9h6/LxdT70BfNT5/3sqHTtmLk+yY4f5Rpcu8NFH4OOTBRWLiK3sDkv79u2jbdu2XLt2jZiYGIoXL86FCxcoWLAgpUqVUlgSkXxn1cFwJiw/bHdIsgD+Pp7Uv6s4fPYZDB0KMTFQtCjMng2dOmVFuSJiJ7tbBwwbNoz27dtz6dIlvLy82L59O//88w+1a9dm6tSpWVGjiEiOlTg/yd6glOitB/1wffIJ6NvXDEpNmpgtARSURHIMu8PS/v37GTFiBK6urri6uhIbG0tgYCDvvPMOr776albUKCKSI2VkflKiAB9PvisfycNPt4AffwQ3N3j3XVi3DgIDHV2qiGSC3bfh3NzcrOvB+fn5ERYWRpUqVfDx8SEsLMzhBYqI5DSZmZ8EMLJRIC+u+hSXV2eaO0JCzJYA993n2EJFxCHsDks1a9Zk9+7dVK5cmaZNm/L6669z4cIFvvzyS6pXr54VNYqI5BgZnZ+UaHTADV54qRMcOWLuGDQIpkwxm02KSI5kd1iaNGkS0dHRALz55pv06NGD/v37U7FiReYmNk4TEcmDVv4Zzotf275sye1cEuJ5bteP9N260GwP4O9vNpts3drBVYqIo9ndwVuSUwdvkbxv5Z9nGbhoHwkZ+BezdNQ53lsxnQZhB8wdHTrAp5+Cr69DaxQR+2RZB28Rkfxm1cFwXvx6X4bOffTwJt5aPYsisTHc8ipIgQ/ehz59tK6bSC5id1gKDg62TvBOycmTJzNVkIhITpL4xJu9vGNjeGP1bDoe3gjAlXtrUXTJYqhY0cEVikhWszssDR06NMn2zZs32bdvH6tWreKll15yVF0iIjnCztBLdk/mrnv6INN+nkbZqHMYLi4Yr71G0ddeM9sDiEiuY3dYGjJkSIr7P/roI3bv3p3pgkREcpJz0bYHJbf4mwzb8hX9ti/BBQPjrruwLFyIpUGDLKxQRLKa3U0pU9OmTRuWLFniqMuJiOQIvoU9bDquwsXT/PDlSF7c/j0uGPzbsROW/ftBQUkk13PYBO/vv/+e4sWLO+pyIiJOFZ9gMHP9cb7Yks48TMOg676VjNnwBV63Yon08ubkpOnUHNonewoVkSyXoaaUt0/wNgyDiIgIzp8/z6xZsxxanIiIM6w6GM6oHw5w5drNNI/zjbnMOyvfp9lJcwrClQea4P3NQmqWLZMdZYpINrE7LHXo0CHJtouLCyVLlqRJkybcc889jqpLRCTbJY4mTV/7d7rHPnx8B++u+pDiMVfAwwPefpuigweDi8NmN4hIDqGmlA6gppQiud+qg+GMX3aIiKjYNI/zirvBaxs+o8v+VeaOe+8113WrVi0bqhQRR7L157fdvwKdOXOGDz74gIEDBzJ8+HA+/vhjLl++nKliHW3WrFkEBwfj6elJ7dq12bx5c5rHb9q0idq1a+Pp6cldd93FnDlzsqlSEckJVh0Mp//CvekGperhx/h5/hBrUDre7QXYuVNBSSSPsysszZo1iwoVKjB06FC++uorvvjiC/r370/ZsmVZtGgRYM5h2rcvY51uHWHx4sUMHTqUMWPGsG/fPho1akSbNm0ICwtL8fjQ0FDatm1Lo0aN2LdvH6+++iqDBw/Wk30i+UR8gsH4ZYdJa4jdJSGeAb8v5oeFI6lw6QzhhUvQudNEzo+baN6CE5E8zeawtGLFCgYPHszAgQM5c+YMly9f5sqVK5w5c4YXXniBHj16sGXLFrp06cLy5cuzsuY0TZs2jT59+vDcc89RpUoVZsyYQWBgILNnz07x+Dlz5lCuXDlmzJhBlSpVeO655+jduzdTp07N5spFxBlmrj9GRFTqvZTKXolg8dejeWnzl7glxPPz3Q/SuvdMTt1bj7rBegJYJD+weYL3O++8w6hRo3jrrbeS7A8ICGDatGkULFiQFi1a4O/vz+TJkx1eqC3i4uLYs2cPo0aNSrK/ZcuW/P777ymes23bNlq2bJlkX6tWrfj888+5efMmbil03I2NjSU29n/D9VFRUQ6oXkSy26qD4UxfeyzlNw2Dxw+tZ8KaOXjHXSfa3YtxLfrxQ9VmWCwWprQPwdVF67uJ5Ac2jyzt27ePbt26pfp+t27diI2NZdOmTQQFBTmkOHtduHCB+Ph4/Pz8kuz38/MjIiIixXMiIiJSPP7WrVtcuHAhxXMmT56Mj4+P9RUYGOiYL0BEsk1aa775XI9m5k9TmLZiOt5x19lVJoQ2vT7kh2oPU6yQO7O71qJ1tYBsrlhEnMXmkaWEhIQUR1kSubm54eXlRbly5RxSWGbcudCvYRhpLv6b0vEp7U80evRohg8fbt2OiopSYBLJZVJb863hqf28t2I6AVcvctPFlRkPPMvs+k9SpJAnwx4oz8BmlTSiJJLP2ByWqlatyk8//cSwYcNSfP/HH3+katWqDissI3x9fXF1dU02inTu3Llko0eJ/P39Uzy+QIEClChRIsVzPDw88NCkTpFc7c413zxuxTHytwX03fUjACeKl2FYuxH8GVCZYc0rKSSJ5GM234Z78cUXGTNmDLNmzeLWrVvW/bdu3eKjjz7itdde48UXX8ySIm3l7u5O7dq1WbNmTZL9a9asoWHDhime06BBg2THr169mjp16qQ5kiYiuVspb0/rnyufP8WPC4Zbg9JX97WmXY/3/z8oVWZI88oKSiL5mM0jSz169ODAgQMMHDiQ0aNHU6FCBQBOnDjB1atXGTx4MD179syqOm02fPhwunXrRp06dWjQoAGffPIJYWFh9OvXDzBvoZ05c4YFCxYA0K9fP2bOnMnw4cPp27cv27Zt4/PPP7e2QhCRvKlucHFKe7vTev13vLJpHh7xN7lQ0IeX2wxhfcW6APgX8WBgs4pOrlREnM2u5U6mTp3Kk08+yaJFizh2zHyCpFGjRnTu3Jn69etnSYH2euaZZ7h48SJvvPEG4eHhVKtWjZUrV1onnYeHhyfpuRQcHMzKlSsZNmwYH330EaVLl+aDDz7giSeecNaXICLZ4exZFv0wgaC9WwFYV+F+XmkzmAuFipE4hjT+0aoaURIRLXfiCFruRCR32Tf9M+4aMxyf69FcL+DBW8368NV9beD/H+oI8PFkXPsQPfEmksfZ+vPb7oV0RURyreho/u3el5o/LgbggF8FhrYfyYkS/3uaVZO5ReROWh5bRPKH33/HuO8+yv64mAQszKr/JI93m5okKFmAb3addl6NIpIjKSyJSN528ya8/jpGo0ZYTp7k3yKl6PTsZN5p3JObrkmfeDWA8Mgb7Ay95JxaRSRH0m04Ecm7jh+Hrl1hxw4swA9VmzKuRT+iPQqledqdPZhEJH/LUFi6desWGzdu5MSJEzz77LN4e3tz9uxZihQpQuHChR1do4iIfQyDhE8/wxg2DNdrMUR5FmZMi/4sD2ls0+m392ASEbE7LP3zzz+0bt2asLAwYmNjadGiBd7e3rzzzjvcuHGDOXPmZEWdIiK2OX+e/zp1x2/9KgC2lavO8EeGE16kZLqnWgB/H0/qBhfP4iJFJDexe87SkCFDqFOnDpcvX8bLy8u6v2PHjqxbt86hxYmI2GXVKm6EVMNv/SriXAowqUkvnu000aaglGhc+xA9CSciSdg9srRlyxa2bt2Ku7t7kv1BQUGcOXPGYYWJiNjs+nV4+WWYORNP4O8S5RjWfgSH/CrYfIkShdyZ2LGaeiuJSDJ2h6WEhATi4+OT7f/333/x9vZ2SFEiIjbbtw+6dIEjRwCYW7s9bzfuSayb7YtdFy/kxrbRD+NeQA8Ii0hydv/L0KJFC2bMmGHdtlgsXL16lXHjxtG2bVtH1iYikrr4eHj3XahXD44cIa5kKaYOnc6E5i/YFZQAJnWsrqAkIqmye2Rp+vTpNG3alJCQEG7cuMGzzz7LsWPH8PX11eKzIpI9wsKgRw/YuBGA9fc0ZESLAVz28LH7UsOaV9atNxFJk91hqXTp0uzfv59Fixaxd+9eEhIS6NOnD126dEky4VtEJEt88w306weRkVxz92R8s+f59t4W1nXd7OFfxIOBzSpmQZEikpdoIV0H0EK6ItkgMhIGDICvvgJgX8DdDG0/gn+Klbb7UomxanbXWhpVEsnHHLqQ7rJly2z+4EcffdTmY0VEbBG/cRO3unTF4+y/xFtc+LDhM8xs8Ay3XDO2CIG/jyfj2ocoKImITWz6l6ZDhw42XcxisaT4pJyISEbE34hlb6/B1P7mUzww+KeoP8PajWBvmSoZut7AphV5oKIvdYOLq5eSiNjMprCUkJCQ1XWIiCSxedlvlOjXh/vDjwOwuHoL3ni4LzEeBe2+VmJn7mEtKiskiYjdtJCuiOQshsGhsW9TZ8oEvG7FctnTm1GtB/Hr3Q0zdLnEaKTO3CKSURlqLLJu3TratWtHhQoVqFixIu3atWPt2rWOrk1E8pv//sN4pB1VJ76K161Yfitfk1a9Z2Y4KIE5oqSJ3CKSGXaPLM2cOZNhw4bx5JNPMmTIEAC2b99O27ZtmTZtGgMHDnR4kSKSDyxfDn36YDl/nlhXN95u0pN5tdtjWOz/na6whyvP1AmkeYi/5ieJSKbZ3TqgTJkyjB49Olko+uijj5g4cSJnz551aIG5gVoHiGRCTAyMGAEffwxAZKUqPNVoAH+XLG/3pYp6udHrgfIMbFZJAUlE0mXrz2+7f2WLioqidevWyfa3bNmSqKgoey8nIvnZrl1Qs6Y1KDF8OEd+XJuhoDSseSX2jG3BkOaaxC0ijmV3WHr00UdZunRpsv0//fQT7du3d0hRIpLH3boFb70FDRvCsWMYZcpw6Msf+KnbcG66ulG8kLvNlwrw8WRO11oKSSKSZeyes1SlShUmTpzIxo0badCgAWDOWdq6dSsjRozggw8+sB47ePBgx1UqInlDaCh06wZbtwIQ3qo9Pe/vxdGD7nBwv02X0JwkEclOds9ZCg4Otu3CFgsnT57MUFG5jeYsidjAMGDBAhg0CKKjoUgR/hg1kQ5XymPYuK6b5iSJiCM5dLmT24WGhmaqMBHJhy5dMhe//e47c/vBB4mfv4B+i09iWG7YdInihdzYPro57gUy1PFERCTD9K+OiGStdevg3nvNoFSgAEycCBs3stMoQnikbUEJ4FLMTfb8czkLCxURSZndI0uGYfD999+zYcMGzp07l2wplB9++MFhxYlILhYbC2PGwHvvmduVK8NXXxFfqzY7Qy8xZ9Nxuy95Ltr2cCUi4ih2h6UhQ4bwySef0LRpU/z8/LDYONdARPKRAwegSxfzf4GEF15g14BX+fVUND9OXMulmLgMXbaUt6cjqxQRsYndYWnhwoX88MMPtG3bNivqEZHcLCEBPvgARo0yR5ZKlmTP6+8yMLos4V8dyPBlExfCrRtc3HG1iojYyO45Sz4+Ptx1111ZUYuI5GZnzkCrVjBsmBmUHnmE9d+u5cl/fe2am3QnLYQrIs5md1gaP348EyZM4Pr161lRj4jkRkuWmJO4164FLy+YNYv4n5YxZtt57OpNkgIthCsizmb3bbinnnqKRYsWUapUKcqXL4+bm1uS9/fu3euw4kQkh4uOhsGDYd48c7tWLfjqK7jnHnaeuJipEaWBTSvyQEVfNZ0UEaezOyz17NmTPXv20LVrV03wFsnPtm2Drl3h5EmwWMx5SuPHg7u5VElGn1xLnJ80rIWWLxGRnMHusLRixQp+/fVXHnzwwayoJ8NOnTrFm2++yfr164mIiKB06dJ07dqVMWPG4O6e+jpTPXv2ZP78+Un21atXj+3bt2d1ySK5082b5rpub71lTugOCoIvv4RGjZIclpEn1zQ/SURyIrvDUmBgYI5c0uOvv/4iISGBjz/+mIoVK3Lw4EH69u1LTEwMU6dOTfPc1q1bM3fuXOt2WuFKJF87dswcTdq509zu2hVmzgQfn2SH1g0uToCPJxGRN2yet+Tv48m49iGanyQiOYrdYem9997j5ZdfZs6cOZQvXz4LSsqY1q1b07p1a+v2XXfdxdGjR5k9e3a6YcnDwwN/f/+sLlEk9zIM+OwzGDoUrl2DokVh9mzo1CnVU1xdLIxrH0L/hXuxQKqBqXghNzreV0aL4opIjmV3WOratSvXrl2jQoUKFCxYMNkE70uXLjmsuMyKjIykePH0+7Js3LiRUqVKUbRoURo3bszEiRMpVapUqsfHxsYSGxtr3Y6KinJIvSI50oUL8Nxz8NNP5nbTpjB/PgQGpnlafIKBj5c7vR4oz4/7zyZpRKmAJCK5id1hacaMGVlQhuOdOHGCDz/8kPcSl1pIRZs2bXjqqacICgoiNDSUsWPH0qxZM/bs2YOHh0eK50yePJkJEyZkRdkiOcuqVdCrF0REgJsbTJoEw4eDS9pdR1YdDGfC8sNJnoZTQBKR3MpiGEZm26BkqcS+TmnZtWsXderUsW6fPXuWxo0b07hxYz777DO7Pi88PJygoCC++eYbHn/88RSPSWlkKTAwkMjIyBw5n0vEbtevw8svm/ORAEJCzJYA992X7qmrDobTf+HeZLfdEqOReiaJSE4RFRWFj49Puj+/7R5Zut3169e5efNmkn2ODgsDBw6kUxrzIoAkc6fOnj1L06ZNadCgAZ988ondnxcQEEBQUBDHjh1L9RgPD49UR51Ecr19+8x13Y4cMbcHD4a33zabTaYgPsFgZ+glzkXfoLiXO68uPZji/CQDMzBNWH6YFiH+GlkSkVzD7rAUExPDK6+8wrfffsvFixeTvR8fH++QwhL5+vri6+tr07FnzpyhadOm1K5dm7lz5+KSzq2ClFy8eJHTp08TEKDffCWfiY+H996D114z2wP4+5vNJlu1Sn7o/wekNYcjks1HSosBhEfeYGfoJRpUKOHY+kVEsojdaeLll19m/fr1zJo1Cw8PDz777DMmTJhA6dKlWbBgQVbUaJOzZ8/SpEkTAgMDmTp1KufPnyciIoKIiIgkx91zzz0sXboUgKtXrzJy5Ei2bdvGqVOn2LhxI+3bt8fX15eOHTs648sQcY6wMGjeHF55xQxKHTrAgQMpBqVVB8N5cMp6On+6nS+2nrI5KN0uow0rRUScwe6RpeXLl7NgwQKaNGlC7969adSoERUrViQoKIivvvqKLl26ZEWd6Vq9ejXHjx/n+PHjlC1bNsl7t0/LOnr0KJGRkQC4urpy4MABFixYwJUrVwgICKBp06YsXrwYb2/vbK1fxGkWLYL+/SEyEgoVgvffh969za7cd0htPpK9MtKwUkTEWewOS5cuXSI4OBgw5ycltgp48MEH6d+/v2Ors0PPnj3p2bNnusfdHpy8vLz49ddfs7AqkRzsyhUYMAC+/trcrlcPFi6EihVTPDw+wWDC8sOZCkqJS5nUDU6/pYeISE5h9224u+66i1OnTgEQEhLCt99+C5gjTkWLFnVkbSKSVTZtgho1zKDk6mqu6bZlS6pBCWBn6KVMLYybSEuZiEhuY3dY6tWrF3/88QcAo0ePts5dGjZsGC+99JLDCxQRB4qLMxe8bdrUnKdUoYIZksaNgwJpDzRndp5RiULuahsgIrmS3bfhhg0bZv1z06ZNOXLkCHv27KFChQrUqFHDocWJiAMdOWK2BNi3z9zu0wemTwcb5+dlZp5R8UJubBv9MO4F7H9CVUTE2TLVZwkgKCiIoKAgR9QiIlnBMGDWLBg5Em7cgBIl4NNPwc4nPmsHFaN4IXe7nn5LvNk2qWN1BSURybVs/tdrx44d/PLLL0n2LViwgODgYEqVKsXzzz+fpKu1iOQAERHwyCMwcKAZlFq2hD//tDkoxScYbDtxkTeWH6L+5HV2twnw9/HUrTcRyfVsHlkaP348TZo0oU2bNgAcOHCAPn360LNnT6pUqcK7775L6dKlGT9+fFbVKiL2+OkncwHcCxfAwwPeeccMTTY2a01pfbfUJK771uweP7DAhauxlPL21BpwIpIn2ByW9u/fz5tvvmnd/uabb6hXrx6ffvopAIGBgYwbN05hScTZYmJg2DDzVhvAvfeaT71VrWrT6fEJBjPXH2f62r9tOr54ITe2j26u22wikmfZHJYuX76Mn5+fdXvTpk20bt3aun3//fdz+vRpx1YnIvbZuRO6doXEtQ1HjoS33jJHltJw+/IlS/ed4fK1m2kef7tLMTfZ889lLV8iInmWzWHJz8+P0NBQAgMDiYuLY+/evUyYMMH6fnR0NG5ubllSpIik49Ytc7Hb8ePNNd7KlIEFC6BZs3RPted2W2q0fImI5GU2h6XWrVszatQopkyZwo8//kjBggVp1KiR9f0///yTChUqZEmRIpKG0FDo1g22bjW3n34a5syBYsXSPM3e221p0fIlIpKX2RyW3nrrLR5//HEaN25M4cKFmT9/Pu7u7tb3v/jiC1q2bJklRYpICgzDHD0aNAiio81+SbNmmb2UUljX7XarDoYzftkhIqIy9wSrli8RkfzA5rBUsmRJNm/eTGRkJIULF8bV1TXJ+9999x2FCxd2eIEikoJLl+CFF+D7783tRo3M4FS+fJqnOXI0KTGOafkSEcnr7G5K6ePjk+L+4sX1m6VItli7Fnr0gLNnzSVK3ngDXn7ZXOMtDY4aTUrk7+PJuPYh6qEkInlepjt4i0g2uXEDXn3VXKIE4O67YeFCqFMn1VNuf8rti62nMl1CYj+l5iH+6qEkIvmGwpJIbnDggDkX6cABc7t/f5g6FQoWTPUURzzldrthzSsxsFklBSQRyXcUlkRysoQEeP99GDUK4uKgZEn44gto1y7N01YdDKf/wr0YDighQLfbRCSfU1gSyanOnIGePc05SmCu8fb553Bbc9iUxCcYTFh+OFNBSbfbRET+R2FJJCdasgSef9586s3LC6ZNM59+S6clAMD2kxczdetNt9tERJJSWBLJSaKiYMgQmDfP3K5VC776Cu65J9VTEidxn4u+wakL1/hia2iGPlq320REUqawJJJT/P67ua5baKg5gjRqlLl8yW3NX+/kqEncGk0SEUmdwpKIs928CW++CRMnmhO6g4Lgyy/NRpNpcMQkbo0miYikT2FJxJmOHTNHk3buNLe7doWZMyGV5q+JMjuJu88D5TV5W0TERgpLIs5gGPDZZzB0KFy7BkWLwuzZ0KlTuqfGJxjM2xqaoVtvRQu68fbj1TWSJCJiB4Ulkex2/jz07Qs//WRuN20K8+dDYGC6p2Z2jtJHnWvxQCXfDJ0rIpJfKSyJZKdffoFeveC//8DNDSZNguHDwcUl3VMzM0fJgrmWW/0KJTJwtohI/qawJJIdrl83F7udOdPcDgmBr7+GGjVsOj0zc5QSZySNax+i+UkiIhmQ/q+zIpI5+/ZB7dr/C0qDB8Pu3TYHJYCdoZcyfOvN38eT2V1raZ6SiEgGaWRJJKvEx5uL3Y4da7YH8Pc3m022amX3pc5F2x6U/It40LluOcr7FqKUt6eeeBMRySSFJZGsEBYG3bvDpk3mdocO8Omn4JuxydWlvD1tOm7sI1Xo+UCwwpGIiAPpNpyIo339Ndx7rxmUChUyF7/94YcMByWAusHFCfDxJLUIZMFsMKmgJCLieApLIo5y5Qp06WK+IiOhfn344w/o3dumBXDT4upiYVz7EIBkgUkTuEVEspbCkogjbNpkTtj++mtwdTXXdNu8GSpUcMjl4xMMfLzc6fVAeYoVSrpWnCZwi4hkrTwVlsqXL4/FYknyGjVqVJrnGIbB+PHjKV26NF5eXjRp0oRDhw5lU8WS68XFwejRZmPJsDAzHG3ZAuPGQQHHTAlcdTCcB6esp/On2/li6ykuxcRRvJAbfR4oz6K+9dnySjMFJRGRLJSnwhLAG2+8QXh4uPX12muvpXn8O++8w7Rp05g5cya7du3C39+fFi1aEB0dnU0VS6515Ag0aABvv20uX9Knj9kmoH59h31EYiPKO9sGXI65yRdbTxF5PU633kREslieC0ve3t74+/tbX4ULF071WMMwmDFjBmPGjOHxxx+nWrVqzJ8/n2vXrvH1119nY9WSqxgGfPQR1KoFe/dC8eKwZIm51pu3t92Xi08w2HbiIj/tP8O2ExeJTzCITzDYeuwCo5YcSLERZeK+CcsPE5+Q0eV0RUTEFhbDMPLMv7Tly5cnNjaWuLg4AgMDeeqpp3jppZdwd3dP8fiTJ09SoUIF9u7dS82aNa37H3vsMYoWLcr8+fNTPC82NpbY2FjrdlRUFIGBgURGRlKkSBHHflGSs0REmBO2f/nF3G7ZEubOhdKlM3S5lNZ6K1rQDYAr127adI1FfevTQMuYiIjYLSoqCh8fn3R/fuepPktDhgyhVq1aFCtWjJ07dzJ69GhCQ0P57LPPUjw+IiICAD8/vyT7/fz8+Oeff1L9nMmTJzNhwgTHFS65w7Jl5q22CxfAwwPeeQcGDrRpXbfbxScY7Ay9xJrDEXyx9VSy920NSYnsaVgpIiL2y/Fhafz48ekGk127dlGnTh2GDRtm3XfvvfdSrFgxnnzySaZMmUKJEqn/5m2547FuwzCS7bvd6NGjGT58uHU7cWRJ8qiYGBg2zGwqCeZTb199BVWr2n2plEaSMsvWhpUiIpIxOT4sDRw4kE6dOqV5TPny5VPcX///J9oeP348xbDk7+8PmCNMAQH/e5ro3LlzyUabbufh4YGHh0d6pUtesHMndO0Kx46ZvZJGjIC33jJHluyUOFnbUfe9LZhtA+oGF3fQFUVEJCU5Piz5+vrim8HOx/v27QNIEoRuFxwcjL+/P2vWrLHOWYqLi2PTpk1MmTIlYwVL3nDrlvmU2/jx5hpvZcvCggVmi4AMiE8wmLD8sEODEqgRpYhIdsjxYclW27ZtY/v27TRt2hQfHx927drFsGHDePTRRylXrpz1uHvuuYfJkyfTsWNHLBYLQ4cOZdKkSVSqVIlKlSoxadIkChYsyLPPPuvEr0acKjQUunWDrVvN7WeegdmzoVixDF9yZ+glh9568/fxZFz7EPVXEhHJBnkmLHl4eLB48WImTJhAbGwsQUFB9O3bl5dffjnJcUePHiUyMtK6/fLLL3P9+nVefPFFLl++TL169Vi9ejXeGXgEXHI5wzBHjwYNguhoKFLEbBHQpUumlytx1CTsol5ufNSlFvXvKqERJRGRbJKnWgc4i62PHkoOdukSvPACfP+9uf3gg/Dll5DKfDh7bTtxkc6fbs/w+YmxSMuaiIg4jq0/v/NcU0oRu61dC9Wrm0GpQAGYNAk2bnRYUIpPMEhIMCjq5WbT8UULull7LSXS+m8iIs6TZ27Didjtxg0YMwamTTO3K1c2WwLUqeOwj7CnVUCfB8rTPMTf+nTbztBLnIu+QSlv84k33XYTEXEOhSXJnw4cMOciHThgbvfrB1OnQqFCmbpsYsPJc9E3OHXhGjPW/p3uE3ABqUzWVlduEZGcQWFJ8peEBPjgAxg1CmJjoWRJ+OILaNcu05e2t+GkJmuLiOQOCkuSf5w5Az17mnOUAB55BD7/HNJoQGqrjDScvHL9Ji4Wi4KSiEgOp7Ak+cP338Pzz8Ply+DlZc5TeuGFTLUESLzlFhF5nTdXHMlQw0mt6yYikvMpLEneFh0NgwfDvHnmdu3a5iTuu++26zK3z0Uq5e3J5Zg43lyR+TXetK6biEjOp7Akedfvv5vruoWGgosLjB4Nr78O7u52XSYrFr/Vum4iIrmHwpLkPTdvwptvwsSJ5oTuoCCzwWSjRnZfytGL34LWdRMRyW0UliRvOXbMHE3audPc7tYNPvwQfHzsvpSjF79NpHXdRERyF4UlyRsMAz77DIYOhWvXoGhRmDPHXATXDrfPTboQHZvpW28WwACGNa9Eed9CajApIpILKSxJ7nf+PPTtCz/9ZG43bQrz50NgYLKJ2YlBJaX9aw5HOHxukkaRRERyP4UlydFSCzvW91esJL5nL9wvnCPBzR0mTcRl+HBwcUlxYnaAjyeP1ghg2R/hSfYXLejGlWs3HVJz8UJujG1XFf8iGkUSEckLFJbEadILQqmFnXHtQ2hdoSj/9BlA0KK5uAJ/lyjHkEdHcuVmCOMO/weQ4sTs8MgbfPxbaLJaHBGUEiuf1LG6RpJERPIQi2EYjp6/mu9ERUXh4+NDZGQkRYoUcXY5TpVeAEqUZhCqFpDqU2gWIOS/E8xf9z6+p08C8EXtR5nSuAexbh7WOUKOHCmyVWprvImISM5k689vjSyJw6QXgG4/LqUgFBF5g/4L9/LRszVT7IjtkhDP8zuXMnzzQtwTbnGuUDFGth3Kb3fVth6TeE5WB6UAH0/GPlKFYoU80g2GIiKSu2lkyQE0spR6AEqMDrO71qJ1tQDiEwwenLI+1UnUFqBYITcuxSQNO6WjzjHt52nUP33Q/LzKDRjdaiCXC9rfEiCjxj5SBV9vDwUjEZE8QiNLkm3S6kdkYAagCcsP0yLEn52hl9J82syAZEHp0cObeGv1LIrExhDj5sn45s/zXfUWmVrXzR6J3bZ7PhCsgCQikg8pLEmm2RKAwiNvWOcy2arIjau8sWY2HQ5vAmBv6bsZ2m4kYcWyb06Qum2LiIjCkqTK1snatgagxOvYovm5v5iwZAplos5zy+LCzIbP8GHDTsS7uALgYjH7UKY0mmUBfAq6Efn/85Zsuc+c2sRw9UkSERGFJUmRrZO1AZsDUGLgCvDxJCLyRoohxj3+Jq/t/IZum7/FYhicKhrAsHYj2FfmHuB/Iz19GwXzyW+h1pCTKPH9tx+vDmBzn6XEUJR4q1CTtkVEJJEmeDtAXpvgbetk7USJk7ZTC0CJc362vNIMVxeL9fqQNOhUvHCa95e/S9VzZkuA0493pmf1zpy44WI95s72AukFOns6eCsUiYjkL7b+/FZYcoC8FJZseVrt9uCTKLUAlFrAShJ0DINu+1bw2oYv8LgVByVKwKefQseO6XfwVugREZEMUljKRjktLGUmQGw7cZHOn25P97hFfevToEKJJPvsuXWXWOe+nUcIHDEAv983mjtbtoS5c6F0aZvqFRERySi1Dsin7A0sd7JnsvadWlcLsGvOj+vyZdR57jm4cAE8PODdd2HAAHBxSfF4ERERZ1BYykPS64x9562wlNgzWTslri6WZCNOyVy9CsOGwWefmds1asBXX0HVqjZ9toiISHbSr/B5RHqNIcF8Miw+Ie27rolPq6V2086COVJVN7h4xgrduRNq1jSDksUCL70EO3YoKImISI6lsJRH2NMYMi2uLhbGtQ8BSBaYMtWg8dYtePNNaNgQjh+HsmVh3Tp45x3zFpyIiEgOpbCUDeITDLaduMhP+8+w7cTFdEd3MiIzc43u1LpaALO71sLfJ+mtNn8fT5tu5SVz8iQ0bgyvvw7x8fDMM/Dnn9C0qX3XERERcQLNWcpimZ1wbavMzjW6k72TtVNkGDB/PgwaZM5TKlIEPvoIunTJtnXdREREMkthKQs5YsK1rdLrjJ3YH8meuUY2TdZOzcWL0K8ffP+9ud2oESxYAOXLZ+x6IiIiTqLbcFnEUROubZVlc40yYu1auPdeMygVKACTJsGGDQpKIiKSKyksZRFHTbi2h8PnGtnrxg0YPhxatICzZ+Huu2H7dhg9Glxds/azRUREskieuQ23ceNGmqYyYXjnzp3cf//9Kb7Xs2dP5s+fn2RfvXr12L49/S7WaXHkhGt7OGSuUUYcOGDORTpwwNzu1w/eew8KFszazxUREclieSYsNWzYkPDw8CT7xo4dy9q1a6lTp06a57Zu3Zq5c+dat93d3TNdj6MnXNsjU3ON7JWQAO+/D6NGQVwclCoFX3wBjzySPZ8vIiKSxfJMWHJ3d8ff39+6ffPmTZYtW8bAgQOxpPPklYeHR5JzHSErJlznOGfOQI8eZr8kgHbt4PPPzcAkIiKSR+TZOUvLli3jwoUL9OzZM91jN27cSKlSpahcuTJ9+/bl3LlzaR4fGxtLVFRUktedctSE66zw/fdQvboZlLy8YM4cWLZMQUlERPIci2EYju+QmAO0bdsWgJUrV6Z53OLFiylcuDBBQUGEhoYyduxYbt26xZ49e/BIpbP0+PHjmTBhQrL9Ka1anF19lrJNVBQMHmz2TwKoXdtc1+3uu51bl4iIiJ2ioqLw8fFJ8ef37XJ8WEotmNxu165dSeYl/fvvvwQFBfHtt9/yxBNP2PV54eHhBAUF8c033/D444+neExsbCyxsbHW7aioKAIDA1P9y45PMLJ/wnVW2LoVunWD0FBwcTGfchs3DtzcnF2ZiIiI3WwNSzl+ztLAgQPp1KlTmseUv6N/z9y5cylRogSPPvqo3Z8XEBBAUFAQx44dS/UYDw+PVEedUpKtE66zws2b8MYbZr+khAQICoIvvzQbTYqIiORxOT4s+fr64uvra/PxhmEwd+5cunfvjlsGRjwuXrzI6dOnCQjIhbfIssLff0PXrrBrl7ndvTt88AH4+Di3LhERkWyS5yZ4r1+/ntDQUPr06ZPi+/fccw9Lly4F4OrVq4wcOZJt27Zx6tQpNm7cSPv27fH19aVjx47ZWXbOYxjwySdQs6YZlIoWhcWLzblKCkoiIpKP5PiRJXt9/vnnNGzYkCpVqqT4/tGjR4mMjATA1dWVAwcOsGDBAq5cuUJAQABNmzZl8eLFeHt7Z2fZOcv58/Dcc+bTbQBNm5ohKTDQuXWJiIg4QY6f4J0b2DpBLFdYuRJ694b//gN3d3Oe0rBh5oRuERGRPCTPTPCWbHLtGrz0EsyaZW5XrWq2BKhRw7l1iYiIOJmGCwT27jX7JSUGpSFDzHlKCkoiIiIKS/lafDxMmQL168Nff0FAAPz6K8yYYXblFhEREd2Gy7f++cdsA/Dbb+Z2x47m0292tGkQERHJDzSylB999RXce68ZlAoXhi++gCVLFJRERERSoJGl/OTKFXjxRVi0yNyuXx8WLoQKFZxaloiISE6mkaX8YuNGczRp0SJwdYXx42HzZgUlERGRdGhkKa+LjYXXX4d33zW7cleoYI4m1a/v7MpERERyBYWlvOzwYejSBfbvN7f79DGfdCtc2JlViYiI5Cq6DZcXGQbMnGn2Ttq/H0qUgB9+gM8+U1ASERGxk0aW8pqICOjVC1atMrdbtYK5c80eSiIiImI3jSzlJT/9BNWrm0HJwwPef99c601BSUREJMM0spQXXL1qLnb72Wfmdo0aZi+lqlWdW5eIiEgeoJGl3G7HDqhZ0wxKFou5GO6OHQpKIiIiDqKRpdzq1i2YNAneeMNc461sWViwAJo2dXZlIiIieYrCUm508iR07QrbtpnbzzwDs2dDsWLOrUtERCQP0m243MQwYN48c07Stm1QpIjZYHLRIgUlERGRLKKRpdzi4kV44QVzwVuARo3M227lyzu1LBERkbxOI0u5wZo15rpuS5ZAgQLmXKUNGxSUREREsoFGlnKyGzdg9GhziRKAu+82WwLUru3UskRERPIThaWc6s8/zXXdDh40t/v3h6lToWBB59YlIiKSz+g2XE6TkADTpsH995tBqWRJWL4cZs1SUBIREXECjSzlJP/+Cz17wrp15na7dmazST8/p5YlIiKSn2lkKaf47jtzEve6deDlBXPmwLJlCkoiIiJOppElZ4uKgsGDYf58c7t2bXMS9913O7cuERERATSy5Fxbt8J995lBycUFxoyB339XUBIREclBNLLkDDdvmmu6TZpkTugOCoIvvzQbTYqIiEiOorCU3f7+21zXbdcuc7tbN/jwQ/DxcW5dIiIikiLdhssuhgGffAI1a5pBqWhR+OYbc8kSBSUREZEcSyNL2cEwoHNnWLzY3G7WzJynVLasc+sSERGRdGlkKTtYLNCwIbi7m12416xRUBIREcklNLKUXQYNgtatoXJlZ1ciIiIidtDIUnaxWBSUREREcqFcE5YmTpxIw4YNKViwIEWLFk3xmLCwMNq3b0+hQoXw9fVl8ODBxMXFpXnd2NhYBg0ahK+vL4UKFeLRRx/l33//zYKvQERERHKjXBOW4uLieOqpp+jfv3+K78fHx/PII48QExPDli1b+Oabb1iyZAkjRoxI87pDhw5l6dKlfPPNN2zZsoWrV6/Srl074uPjs+LLEBERkVzGYhiG4ewi7DFv3jyGDh3KlStXkuz/5ZdfaNeuHadPn6Z06dIAfPPNN/Ts2ZNz585RpEiRZNeKjIykZMmSfPnllzzzzDMAnD17lsDAQFauXEmrVq1SrCE2NpbY2FjrdlRUFIGBgURGRqb4OSIiIpLzREVF4ePjk+7P71wzspSebdu2Ua1aNWtQAmjVqhWxsbHs2bMnxXP27NnDzZs3admypXVf6dKlqVatGr///nuqnzV58mR8fHysr8DAQMd9ISIiIpKj5JmwFBERgZ+fX5J9xYoVw93dnYiIiFTPcXd3p1ixYkn2+/n5pXoOwOjRo4mMjLS+Tp8+nfkvQERERHIkp4al8ePHY7FY0nzt3r3b5utZLJZk+wzDSHF/WtI7x8PDgyJFiiR5iYiISN7k1D5LAwcOpFOnTmkeU758eZuu5e/vz44dO5Lsu3z5Mjdv3kw24nT7OXFxcVy+fDnJ6NK5c+do2LChTZ8rIiIieZtTw5Kvry++vr4OuVaDBg2YOHEi4eHhBAQEALB69Wo8PDyoXbt2iufUrl0bNzc31qxZw9NPPw1AeHg4Bw8e5J133nFIXSIiIpK75Zo5S2FhYezfv5+wsDDi4+PZv38/+/fv5+rVqwC0bNmSkJAQunXrxr59+1i3bh0jR46kb9++1ttkZ86c4Z577mHnzp0A+Pj40KdPH0aMGMG6devYt28fXbt2pXr16jRv3txpX6uIiIjkHLlmuZPXX3+d+fPnW7dr1qwJwIYNG2jSpAmurq6sWLGCF198kQceeAAvLy+effZZpk6daj3n5s2bHD16lGvXrln3TZ8+nQIFCvD0009z/fp1Hn74YebNm4erq2v2fXEiIiKSY+W6Pks5ka19GkRERCTnyHd9lkRERESygsKSiIiISBpyzZylnCzxTmZUVJSTKxERERFbJf7cTm9GksKSA0RHRwNo2RMREZFcKDo6Gh8fn1Tf1wRvB0hISODs2bN4e3vb3S08uyUu+nv69GlNRs9h9L3JmfR9yZn0fcm5ctP3xjAMoqOjKV26NC4uqc9M0siSA7i4uFC2bFlnl2EXLdOSc+l7kzPp+5Iz6fuSc+WW701aI0qJNMFbREREJA0KSyIiIiJpUFjKZzw8PBg3bhweHh7OLkXuoO9NzqTvS86k70vOlRe/N5rgLSIiIpIGjSyJiIiIpEFhSURERCQNCksiIiIiaVBYEhEREUmDwlI+derUKfr06UNwcDBeXl5UqFCBcePGERcX5+zSBJg4cSINGzakYMGCFC1a1Nnl5FuzZs0iODgYT09PateuzebNm51dUr7322+/0b59e0qXLo3FYuHHH390dkkCTJ48mfvvvx9vb29KlSpFhw4dOHr0qLPLchiFpXzqr7/+IiEhgY8//phDhw4xffp05syZw6uvvurs0gSIi4vjqaeeon///s4uJd9avHgxQ4cOZcyYMezbt49GjRrRpk0bwsLCnF1avhYTE0ONGjWYOXOms0uR22zatIkBAwawfft21qxZw61bt2jZsiUxMTHOLs0h1DpArN59911mz57NyZMnnV2K/L958+YxdOhQrly54uxS8p169epRq1YtZs+ebd1XpUoVOnTowOTJk51YmSSyWCwsXbqUDh06OLsUucP58+cpVaoUmzZt4qGHHnJ2OZmmkSWxioyMpHjx4s4uQ8Tp4uLi2LNnDy1btkyyv2XLlvz+++9Oqkok94iMjATIMz9TFJYEgBMnTvDhhx/Sr18/Z5ci4nQXLlwgPj4ePz+/JPv9/PyIiIhwUlUiuYNhGAwfPpwHH3yQatWqObsch1BYymPGjx+PxWJJ87V79+4k55w9e5bWrVvz1FNP8dxzzzmp8rwvI98bcS6LxZJk2zCMZPtEJKmBAwfy559/smjRImeX4jAFnF2AONbAgQPp1KlTmseUL1/e+uezZ8/StGlTGjRowCeffJLF1eVv9n5vxHl8fX1xdXVNNop07ty5ZKNNIvI/gwYNYtmyZfz222+ULVvW2eU4jMJSHuPr64uvr69Nx545c4amTZtSu3Zt5s6di4uLBhqzkj3fG3Eud3d3ateuzZo1a+jYsaN1/5o1a3jsscecWJlIzmQYBoMGDWLp0qVs3LiR4OBgZ5fkUApL+dTZs2dp0qQJ5cqVY+rUqZw/f976nr+/vxMrE4CwsDAuXbpEWFgY8fHx7N+/H4CKFStSuHBh5xaXTwwfPpxu3bpRp04d68hrWFiY5vU52dWrVzl+/Lh1OzQ0lP3791O8eHHKlSvnxMrytwEDBvD111/z008/4e3tbR2V9fHxwcvLy8nVZZ5aB+RT8+bNo1evXim+p/9LOF/Pnj2ZP39+sv0bNmygSZMm2V9QPjVr1izeeecdwsPDqVatGtOnT88Tj0HnZhs3bqRp06bJ9vfo0YN58+Zlf0ECJJ/fl2ju3Ln07Nkze4vJAgpLIiIiImnQJBURERGRNCgsiYiIiKRBYUlEREQkDQpLIiIiImlQWBIRERFJg8KSiIiISBoUlkRERETSoLAkIiIikgaFJRFJ06lTp7BYLNYlV3KL8uXLM2PGDIddr0mTJgwdOtRh13Mmi8XCjz/+COTe769IdlJYEsnHLBZLmq/csEzBvHnzKFq0aLL9u3bt4vnnn8/WWq5fv864ceO4++678fDwwNfXlyeffJJDhw5lax2Jxo8fz3333Zdsf3h4OG3atMn+gkRyKS2kK5KPhYeHW/+8ePFiXn/9dY4ePWrd5+XlxeXLl51RGvHx8VgsFlxcMvY7XcmSJR1cUdpiY2Np3rw5YWFhvPfee9SrV4///vuPyZMnU69ePdauXUv9+vWztabUaLFsEftoZEkkH/P397e+fHx8sFgsyfYlOnnyJE2bNqVgwYLUqFGDbdu2JbnW77//zkMPPYSXlxeBgYEMHjyYmJgY6/uXL1+me/fuFCtWjIIFC9KmTRuOHTtmfT9xhOjnn38mJCQEDw8P/vnnH+Li4nj55ZcpU6YMhQoVol69emzcuBEwF1Xt1asXkZGR1tGw8ePHA8lvw125coXnn38ePz8/PD09qVatGj///DMAFy9epHPnzpQtW5aCBQtSvXp1Fi1aZNff5YwZM9i2bRs///wzTz/9NEFBQdStW5clS5ZQpUoV+vTpY12kOqVbeh06dEgykrdw4ULq1KmDt7c3/v7+PPvss5w7d876/saNG7FYLKxbt446depQsGBBGjZsaA278+bNY8KECfzxxx/Wv5vEhWZvvw2XksOHD9O2bVsKFy6Mn58f3bp148KFC9b3v//+e6pXr46XlxclSpSgefPmSb7XInmNwpKI2GTMmDGMHDmS/fv3U7lyZTp37sytW7cAOHDgAK1ateLxxx/nzz//ZPHixWzZsoWBAwdaz+/Zsye7d+9m2bJlbNu2DcMwaNu2LTdv3rQec+3aNSZPnsxnn33GoUOHKFWqFL169WLr1q188803/Pnnnzz11FO0bt2aY8eO0bBhQ2bMmEGRIkUIDw8nPDyckSNHJqs9ISGBNm3a8Pvvv7Nw4UIOHz7M22+/jaurKwA3btygdu3a/Pzzzxw8eJDnn3+ebt26sWPHDpv/fr7++mtatGhBjRo1kux3cXFh2LBhHD58mD/++MPm68XFxfHmm2/yxx9/8OOPPxIaGpribdExY8bw3nvvsXv3bgoUKEDv3r0BeOaZZxgxYgRVq1a1/t0888wz6X5ueHg4jRs35r777mP37t2sWrWK//77j6efftr6fufOnenduzdHjhxh48aNPP7442hNdsnTDBERwzDmzp1r+Pj4JNsfGhpqAMZnn31m3Xfo0CEDMI4cOWIYhmF069bNeP7555Oct3nzZsPFxcW4fv268ffffxuAsXXrVuv7Fy5cMLy8vIxvv/3W+vmAsX//fusxx48fNywWi3HmzJkk13744YeN0aNHp1l3UFCQMX36dMMwDOPXX381XFxcjKNHj9r899G2bVtjxIgR1u3GjRsbQ4YMSfV4T0/PVN/fu3evARiLFy9O9VqPPfaY0aNHj1Svv3PnTgMwoqOjDcMwjA0bNhiAsXbtWusxK1asMADj+vXrhmEYxrhx44waNWokuxZgLF261DCM/31/9+3bZxiGYYwdO9Zo2bJlkuNPnz5tAMbRo0eNPXv2GIBx6tSpVGsVyWs0Z0lEbHLvvfda/xwQEADAuXPnuOeee9izZw/Hjx/nq6++sh5jGAYJCQmEhoZy7NgxChQoQL169azvlyhRgrvvvpsjR45Y97m7uyf5nL1792IYBpUrV05SS2xsLCVKlLC59v3791O2bNlk10kUHx/P22+/zeLFizlz5gyxsbHExsZSqFAhmz8jLcb/j7q4u7vbfM6+ffsYP348+/fv59KlSyQkJAAQFhZGSEiI9bjUvi/lypXLUK179uxhw4YNFC5cONl7J06coGXLljz88MNUr16dVq1a0bJlS5588kmKFSuWoc8TyQ0UlkTEJm5ubtY/WywWAOsP8ISEBF544QUGDx6c7Lxy5crx999/p3hNwzCs1wJzQvnt2wkJCbi6urJnzx7rLbNEKf0wT42Xl1ea77/33ntMnz6dGTNmUL16dQoVKsTQoUOJi4uz+TMqVarE4cOHU3zvr7/+ArCGNRcXl2S3rW6/HRkTE0PLli1p2bIlCxcupGTJkoSFhdGqVatkNaX1fcmIhIQE2rdvz5QpU5K9FxAQgKurK2vWrOH3339n9erVfPjhh4wZM4YdO3YQHByc4c8VyckUlkQk02rVqsWhQ4eoWLFiiu+HhIRw69YtduzYQcOGDQFzUvXff/9NlSpVUr1uzZo1iY+P59y5czRq1CjFY9zd3YmPj0+zvnvvvZd///2Xv//+O8XRpc2bN/PYY4/RtWtXwAwMx44dS7O2O3Xu3JkxY8bwxx9/JJm3lJCQwPTp06lTp451RKhkyZJJnkSMj4/n4MGDNG3aFDDD1YULF3j77bcJDAwEYPfu3TbXksiWv5s71apViyVLllC+fHkKFEj5R4TFYuGBBx7ggQce4PXXXycoKIilS5cyfPhwu2sUyQ00wVtEMu2VV15h27ZtDBgwgP3793Ps2DGWLVvGoEGDAHPU5bHHHqNv375s2bKFP/74g65du1KmTBkee+yxVK9buXJlunTpQvfu3fnhhx8IDQ1l165dTJkyhZUrVwLmU29Xr15l3bp1XLhwgWvXriW7TuPGjXnooYd44oknWLNmDaGhofzyyy+sWrUKgIoVK1pHS44cOcILL7xARESEXX8Hw4YNo27durRv357vvvuOsLAwdu3axRNPPMGxY8esT6IBNGvWjBUrVrBixQr++usvXnzxRa5cuWJ9v1y5cri7u/Phhx9y8uRJli1bxptvvmlXPYl/N6Ghoezfv58LFy4QGxub7jkDBgzg0qVLdO7cmZ07d3Ly5ElWr15N7969iY+PZ8eOHUyaNIndu3cTFhbGDz/8wPnz5+0KliK5jcKSiGTavffey6ZNmzh27BiNGjWiZs2ajB071jqHBmDu3LnUrl2bdu3a0aBBAwzDYOXKlUluI6Vk7ty5dO/enREjRnD33Xfz6KOPsmPHDuuIS8OGDenXrx/PPPMMJUuW5J133knxOkuWLOH++++nc+fOhISE8PLLL1tHXcaOHUutWrVo1aoVTZo0wd/fnw4dOtj1d+Dp6cm6devo3r07o0ePpkKFCtStW5eDBw9y8OBBqlataj22d+/e9OjRg+7du9O4cWOCg4Oto0pgjjzNmzeP7777jpCQEN5++22mTp1qVz0ATzzxBK1bt6Zp06aULFnSpnYIpUuXZuvWrcTHx9OqVSuqVavGkCFD8PHxwcXFhSJFivDbb7/Rtm1bKleuzGuvvcZ7772nJpeSp1mMO2+ci4iIQ/zyyy907NiRqVOnJmmjICK5i0aWRESySJs2bfjll1+4dOlSkqaOIpK7aGRJREREJA0aWRIRERFJg8KSiIiISBoUlkRERETSoLAkIiIikgaFJREREZE0KCyJiIiIpEFhSURERCQNCksiIiIiaVBYEhEREUnD/wE5QhzhIxEt6QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot(e_linear, line='s');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Question\n",
    "\n",
    "The errors are from a linear model fitting linear data with noise. Why isn't the plot above showing a straight line, and instead showing a clear pattern?\n",
    "\n",
    "Hint: Show a histogram of the errors and review the documentation of the qqplot graph."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Came from a uniform distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions, see `solutions/why_not_normal.py`*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we plot the QQ plot comparing the residuals to the x values, we get a straighter line and more randomness of the errors around this line. This would lead you to think that the errors are randomly distributed around that line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.gofplots import qqplot_2samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "qqplot_2samples(x, e_linear, line='r');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In other words, this graph shows us that the errors do not seem to be dependent on the x variables.\n",
    "\n",
    "#### Exercise\n",
    "\n",
    "Plot the QQ plots (both against a normal distribution and a 2 sampled QQ plot) for the other datasets we generated in this module. What do their patterns show?\n",
    "\n",
    "#### Extended Exercise\n",
    "\n",
    "When fitting a linear model, a common visualisation is to output the following four graphs in a subplot with two columns and two rows:\n",
    "\n",
    "1. A plot comparing the Predicted values on (x-axis) against the Actual values (y-axis) with a diagonal line\n",
    "1. The residuals (y-axis) versus the x values scatter plot with a horizontal line at y=0\n",
    "1. A QQ plot of the residuals against a normal distribution\n",
    "1. A QQ plot of the residuals against the x values\n",
    "\n",
    "Create a function that takes the necessary inputs and produces these four plots. This function, or variations of it, are incredibly useful for future analysis."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*For solutions see `solutions/residual_analysis_two.py`*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoUAAAHWCAYAAAAB2/MQAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjguNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8fJSN1AAAACXBIWXMAAA9hAAAPYQGoP6dpAADoR0lEQVR4nOydd1hT1xvHvwFC2EuZioCLIe6JVnHvvao4UHHXurVucM+f0rpbBbTuuldRcLfixlVwg2gFFRFQZJmc3x9pYgJJSELGveF8nodHc+d7b+558z3nfc97OYQQAgqFQqFQKBRKmcZI3wZQKBQKhUKhUPQPFYUUCoVCoVAoFCoKKRQKhUKhUChUFFIoFAqFQqFQQEUhhUKhUCgUCgVUFFIoFAqFQqFQQEUhhUKhUCgUCgVUFFIoFAqFQqFQQEUhhUKhUCgUCgVUFGqMqKgocDgc8Z+JiQkqVqyI4cOH499//9WJDZ6enhg2bJj488WLF8HhcHDx4kWVjnP16lWEhYUhMzNTo/YBwLBhw+Dp6anx46pLYWEhXFxcwOFwcPDgQbWPs2fPHoSHh2vOMAUo871OmTIFHA4Hjx49krvN3LlzweFwcOfOHaXPXfQZo1BUQZafdHV1xYABA/D06VOtnTcsLAwcDkepbXXxjKtijz55/PgxLCwsEBQUVGzdx48fUaFCBTRu3Bh8Pl/m/tQPsQ8qCjVMZGQk4uLiEBMTg1GjRmHv3r1o3rw5cnJydG5LvXr1EBcXh3r16qm039WrV7Fw4UKtiEKmcfLkSbx9+xYAsH37drWPo0tRqAwhISEAgIiICJnrBQIBdu7ciTp16qj8fFAopUXkJ2NjYzFhwgQcP34c3333HT5+/KiV840cORJxcXFaObYh4+3tjWXLlmHv3r04dOiQ1Lrx48cjIyMDO3bsgLGxscz9qR9iH1QUahh/f380adIErVq1QmhoKGbOnImkpCQcPXpU7j5fvnzRii02NjZo0qQJbGxstHJ8Q2D79u0wNTVFu3btcPbsWbx+/VrfJmkEf39/NGrUCL///ju+fv1abL3oWkVOm0LRJSI/2bJlS8ydOxezZs3Cu3fvFPrJ0lCxYkU0adJEK8c2dCZNmoQWLVpg3LhxePfuHQDgjz/+wL59+7B06VL4+PjI3Zf6IfZBRaGWETmily9fAhCGT62srPDgwQO0b98e1tbWaNOmDQCgoKAAS5YsgY+PD3g8HhwdHTF8+HC8f/9e6piFhYWYOXMmXFxcYGFhge+++w43btwodm55Ycbr16+jW7duKFeuHMzMzFClShVMnjwZgDCsMWPGDACAl5eXOMwjeYz9+/cjICAAlpaWsLKyQocOHRAfH1/s/FFRUfD29gaPx4Ovry927typ1D3r2bMnPDw8IBAIiq1r3LixVI/yjz/+QOPGjWFrawsLCwtUrlwZI0aMUOo8b968QXR0NLp164YZM2ZAIBAgKipK5rZ79uxBQEAArKysYGVlhTp16ohHFlu2bIlTp07h5cuXUqExQP53kJycDA6HI3W+W7duYcCAAfD09IS5uTk8PT0xcOBA8bOjKiEhIUhLS8Off/5ZbF1kZCR4PB4GDRqEvLw8TJs2DXXq1IGtrS0cHBwQEBCAY8eOlXgOUTgwOTlZarm8646NjUWbNm1gY2MDCwsLNGvWDOfOnZPa5v379xg9ejTc3d3F7aBZs2aIjY1V+R5Q2EGDBg0AQDxqL+LWrVvo3r07HBwcYGZmhrp16+LAgQNS23z58gXTp0+Hl5cXzMzM4ODggAYNGmDv3r3ibWSFa5X1o/JCvbKe/f3796N9+/ZwdXWFubk5fH19MWvWLKUiRefPn0fLli1Rrlw5mJubo1KlSujTp4/CQQNd+EoOh4PIyEh8+fIFY8eORVpaGsaNG4fmzZuLfzcUQf0Qu6CiUMs8e/YMAODo6CheVlBQgO7du6N169Y4duwYFi5cCIFAgB49emDFihUICgrCqVOnsGLFCsTExKBly5bIzc0V7z9q1CisWbMGQ4cOxbFjx9CnTx/07t1bqdDLmTNn0Lx5c6SkpGDt2rX4888/MW/ePLEzHjlyJH788UcAwOHDhxEXFycVgl62bBkGDhwIPz8/HDhwAL///js+ffqE5s2bIyEhQXyeqKgoDB8+HL6+vjh06BDmzZuHxYsX4/z58yXaOGLECKSkpBTb9tGjR7hx4waGDx8OAIiLi8P333+PypUrY9++fTh16hQWLFggs0cqi6ioKPD5fIwYMQJt27aFh4cHIiIiQAiR2m7BggUYNGgQ3NzcEBUVhSNHjiA4OFgs1jZt2oRmzZrBxcVFfL/UCVUlJyfD29sb4eHhOHPmDFauXInU1FQ0bNgQ6enpKh9v4MCBsLCwKBa6+fjxI44dO4ZevXrB3t4e+fn5yMjIwPTp03H06FHs3bsX3333HXr37q20kFeGXbt2oX379rCxscGOHTtw4MABODg4oEOHDlIOeciQITh69CgWLFiAs2fPYtu2bWjbti0+fPigMVsozCIpKQkAUL16dfGyCxcuoFmzZsjMzMSWLVtw7Ngx1KlTB99//71UZ2rq1KnYvHkzJk6ciOjoaPz+++/o169fic9LafyoPJ4+fYrOnTtj+/btiI6OxuTJk3HgwAF069ZN4X7Jycno0qULTE1NERERgejoaKxYsQKWlpYoKCiQu5+ufGXlypWxevVqHDlyBN999x3y8vIQGRkJI6OSJQT1QyyDUDRCZGQkAUCuXbtGCgsLyadPn8jJkyeJo6Mjsba2JmlpaYQQQoKDgwkAEhERIbX/3r17CQBy6NAhqeU3b94kAMimTZsIIYQkJiYSAGTKlClS2+3evZsAIMHBweJlFy5cIADIhQsXxMuqVKlCqlSpQnJzc+Vey+rVqwkAkpSUJLU8JSWFmJiYkB9//FFq+adPn4iLiwvp378/IYQQPp9P3NzcSL169YhAIBBvl5ycTLhcLvHw8JB7bkIIKSwsJM7OziQoKEhq+cyZM4mpqSlJT08nhBCyZs0aAoBkZmYqPJ4sBAIBqVq1KqlQoQL5+vUrIYSQ0NBQAoCcO3dOvN2LFy+IsbExGTRokMLjdenSReZ1yfoOCCEkKSmJACCRkZFyj/n161fy+fNnYmlpSX7++ecSjymL4OBgwuVyydu3b8XL1q9fTwCQmJgYuectLCwkISEhpG7dulLrPDw8pJ4x0XNf9FkpamNOTg5xcHAg3bp1k9qOz+eT2rVrk0aNGomXWVlZkcmTJ5d4bRT2IctPRkdHExcXF9KiRQtSWFgo3tbHx4fUrVtXahkhhHTt2pW4uroSPp9PCCHE39+f9OzZU+F5RW1bhCp+tOi+Ra+l6LMvQiAQkMLCQnLp0iUCgNy7d0/uMQ8ePEgAkLt37yq8jqLowldKXo+Pjw8BQNasWaPSvtQPsQc6UqhhmjRpAi6XC2tra3Tt2hUuLi74888/4ezsLLVdnz59pD6fPHkSdnZ26NatG75+/Sr+q1OnDlxcXMTD3xcuXAAADBo0SGr//v37w8TERKFtT548wfPnzxESEgIzMzOVr+3MmTP4+vUrhg4dKmWjmZkZAgMDxTY+fvwYb968QVBQkFTYxcPDA02bNi3xPCYmJhg8eDAOHz6MrKwsAACfz8fvv/+OHj16oFy5cgCAhg0biq/9wIEDKs3yvnTpEp49e4bg4GBxkvTw4cPB4XCkerQxMTHg8/n44YcflD62unz+/Bk//fQTqlatChMTE5iYmMDKygo5OTlITExU65ghISEoLCzE77//Ll4WGRkJDw8PcdoCIAwtNWvWDFZWVjAxMQGXy8X27dvVPm9Rrl69ioyMDAQHB0s9OwKBAB07dsTNmzfFIbZGjRohKioKS5YswbVr11BYWKgRGyjMQdJPduzYEfb29jh27JjYhz179gyPHj0S+znJZ6Zz585ITU3F48ePAQiflz///BOzZs3CxYsXpaIq8iiNH1XEixcvEBQUBBcXFxgbG4PL5SIwMBAAFLalOnXqwNTUFKNHj8aOHTvw4sULpc6nC18pIjo6Go8ePYKRkZHKIVTqh9gDFYUaZufOnbh58ybi4+Px5s0b3L9/H82aNZPaxsLCotjkj7dv3yIzMxOmpqbgcrlSf2lpaeLwoWjo2sXFRWp/ExMTsQOQhyg3sWLFimpdmyjE3LBhw2I27t+/v0Qb5S2TxYgRI5CXl4d9+/YBEArS1NRUcTgEAFq0aIGjR4+KhWrFihXh7+8vlUskD1E+YK9evZCZmYnMzEzY2triu+++w6FDh8Qzr0t7z1QhKCgIGzZswMiRI3HmzBncuHEDN2/ehKOjo1I/dLJo3rw5qlevjsjISADA/fv3cefOHbEABoRpAv3790eFChWwa9cuxMXF4ebNm+LvQBOInp2+ffsWe3ZWrlwJQggyMjIACPOygoODsW3bNgQEBMDBwQFDhw5FWlqaRmyh6B+Rnzx//jzGjBmDxMREDBw4ULxe9LxMnz692PMyfvx4ABD7m19++QU//fQTjh49ilatWsHBwQE9e/ZUWOKmNH5UHp8/f0bz5s1x/fp1LFmyBBcvXsTNmzdx+PBhAFDYhqtUqYLY2Fg4OTnhhx9+QJUqVVClShX8/PPPJZ5X274SADIzMzFy5Eg0bNgQW7duRXR0tErVGqgfYg/qd4koMvH19RUnTctDVtJy+fLlUa5cOURHR8vcx9raGgDEDistLQ0VKlQQr//69WuJuQ6ivEZ1Z9iWL18eAHDw4EF4eHjI3U7SxqIo26D8/PzQqFEjREZGYsyYMYiMjISbmxvat28vtV2PHj3Qo0cP5Ofn49q1a1i+fDmCgoLg6emJgIAAmcfOysoSl1cQ9aCLsmfPHowfP17qnrm7uytluySiEdn8/Hyp5UVzBLOysnDy5EmEhoZi1qxZ4uWiPJvSMGLECMyaNQs3btzAnj17YGRkJFXja9euXfDy8sL+/fulns2iNstC2esTPTvr16+XOwtUNJpevnx5hIeHIzw8HCkpKTh+/Lh4dqq89kFhF5J+slWrVuDz+di2bRsOHjyIvn37ip+X2bNno3fv3jKP4e3tDQCwtLTEwoULsXDhQrx9+1Y8atitWze59fFU8aOSzziPxxMvL/qMnz9/Hm/evMHFixfFo4MAlC7t1bx5czRv3hx8Ph+3bt3C+vXrMXnyZDg7O2PAgAFy99OmrxTx448/IiMjA7GxsfD19cWRI0cwdepUdOjQQekOM/VD7ICOFDKErl274sOHD+Dz+WjQoEGxP5EDbNmyJQBg9+7dUvsfOHCgxKTh6tWro0qVKoiIiFDY0ESOr2jPtkOHDjAxMcHz589l2ihy8t7e3nB1dcXevXulJm28fPkSV69eVe6GQBjOvX79Ov766y+cOHFCKtQry+bAwECsXLkSAGTOhhaxZ88e5ObmYvHixbhw4UKxv/Lly4tDyO3bt4exsTE2b96s0FYejydzJEBUqPv+/ftSy48fPy71mcPhgBAi9aMDANu2bZNbGFZZgoODYWJigq1bt2L37t1o06aNlKjncDgwNTWVcsRpaWlKzfpT9vqaNWsGOzs7JCQkyH12TE1Nix2/UqVKmDBhAtq1a6dScVsKu1i1ahXs7e2xYMECCAQCeHt7o1q1arh3757c50XUUZbE2dkZw4YNw8CBA/H48WO5M3dV8aPynvETJ05IfRa1n6JteOvWrYovvgjGxsZo3LgxNm7cCABKPffa8pUAcOzYMezatQuLFy+Gr68vAODXX3+FkZERRo0apfR1UT/EDuhIIUMYMGAAdu/ejc6dO2PSpElo1KgRuFwuXr9+jQsXLqBHjx7o1asXfH19MXjwYISHh4PL5aJt27Z4+PAh1qxZo1Q9wo0bN6Jbt25o0qQJpkyZgkqVKiElJQVnzpwRO8iaNWsCAH7++WcEBweDy+XC29sbnp6eWLRoEebOnYsXL16Ic4Hevn2LGzduiHvsRkZGWLx4MUaOHIlevXph1KhRyMzMRFhYmNLhY0A4a23q1KkYOHAg8vPzi1WwX7BgAV6/fo02bdqgYsWKyMzMxM8//yyVxyOL7du3w97eHtOnT5eZWzl06FCsXbsW9+7dQ+3atTFnzhwsXrwYubm5GDhwIGxtbZGQkID09HQsXLhQfM8OHz6MzZs3o379+jAyMkKDBg3g4uKCtm3bYvny5bC3t4eHhwfOnTsnDimJsLGxQYsWLbB69WqUL18enp6euHTpErZv3w47Ozul75ksXFxc0LlzZ0RGRoIQUqwmWNeuXXH48GGMHz8effv2xatXr7B48WK4urqW+JaJhg0bwtvbG9OnT8fXr19hb2+PI0eO4K+//pLazsrKCuvXr0dwcDAyMjLQt29fODk54f3797h37x7ev3+PzZs3IysrC61atUJQUBB8fHxgbW2NmzdvIjo6Wu6IEYX92NvbY/bs2Zg5cyb27NmDwYMHY+vWrejUqRM6dOiAYcOGoUKFCsjIyEBiYiLu3LmDP/74A4Cw9ErXrl1Rq1Yt2NvbIzExEb///jsCAgJgYWEh83yq+NHOnTvDwcEBISEhWLRoEUxMTBAVFYVXr15Jbde0aVPY29tj7NixCA0NBZfLxe7du3Hv3r0Sr3/Lli04f/48unTpgkqVKiEvL0/cMW3btm2J+2vLV6anp2PMmDFo2rQppk6dKl5eoUIFrFu3DsOHD8f27duVqjNI/RBL0OcsF0NCNPvp5s2bCrcLDg4mlpaWMtcVFhaSNWvWkNq1axMzMzNiZWVFfHx8yJgxY8jTp0/F2+Xn55Np06YRJycnYmZmRpo0aULi4uKKzciSN0s1Li6OdOrUidja2hIej0eqVKlSbBbe7NmziZubGzEyMip2jKNHj5JWrVoRGxsbwuPxiIeHB+nbty+JjY2VOsa2bdtItWrViKmpKalevTqJiIggwcHBJc4+liQoKIgAIM2aNSu27uTJk6RTp06kQoUKxNTUlDg5OZHOnTuTK1euyD3evXv3CACFs8oePXpEAEjNst65cydp2LCh+HupW7eu1MzhjIwM0rdvX2JnZ0c4HI7UzMLU1FTSt29f4uDgQGxtbcngwYPJrVu3is0+fv36NenTpw+xt7cn1tbWpGPHjuThw4dKf6+KOHbsGAFAHBwcSF5eXrH1K1asIJ6enoTH4xFfX1/y22+/yZx1WdQWQgh58uQJad++PbGxsSGOjo7kxx9/JKdOnZJp46VLl0iXLl2Ig4MD4XK5pEKFCqRLly7kjz/+IIQQkpeXR8aOHUtq1apFbGxsiLm5OfH29iahoaEkJydH6eulMBNFfjI3N5dUqlSJVKtWTVwR4N69e6R///7EycmJcLlc4uLiQlq3bk22bNki3m/WrFmkQYMGxN7envB4PFK5cmUyZcoU8cxbQmTPIFbWjxJCyI0bN0jTpk2JpaUlqVChAgkNDSXbtm0rNuP16tWrJCAggFhYWBBHR0cycuRIcufOnWJtvag9cXFxpFevXsTDw4PweDxSrlw5EhgYSI4fP670vdW0rySEkH79+hELCwvy5MkTmes7d+5MbGxsSEpKilI2Uj/EfDiEFCnKRqFQKBQKhUIpc9CcQgqFQqFQKBQKFYUUCoVCoVAoFCoKKRQKhUKhUCigopBCoVAoFAqFAioKKRQKhUKhUCigopBCoVAoFAqFAlq8WmkEAgHevHkDa2trma+po1Ao+oMQgk+fPsHNzQ1GRrSvqyzUr1EozEUffo2KQiV58+aNWu++pVAouuPVq1dKv4uVQv0ahcIGdOnXqChUEtF7Nl+9eqXU6+QoFIruyM7Ohru7u8z34VLkQ/0ahcJc9OHXqChUElFoxcbGpsw6T76A4EZSBt59yoOTtRkaeTnA2KjshZzofRDCxPtAQ6CqQf0aM59jCkUSXfo11onCy5cvY/Xq1bh9+zZSU1Nx5MgR9OzZU+E+ly5dwtSpU/HPP//Azc0NM2fOxNixY3VjsIEQ/TAVC08kIDUrT7zMzpyL4c08MaF1tTLjROl9EELvA8UQoM8xhSIN6zKyc3JyULt2bWzYsEGp7ZOSktC5c2c0b94c8fHxmDNnDiZOnIhDhw5p2VLDgC8g+Dn2KcbuuiPlOAEgM7cQ62Kfov6SGEQ/TNWThboj+mEqxtH7QO8DxSA4fT+V+jUKpQgcQgjRtxHqwuFwShwp/Omnn3D8+HEkJiaKl40dOxb37t1DXFyc0ufKzs6Gra0tsrKyykyYJfphKsKO/4O07PwSt+UA2Dy4Hjr6u2rfMD3AFxA0W3Eeadl5Crej90GIru9DWWyfmqCs3rfT999gwt54CEr49TP09kxhNvpon6wbKVSVuLg4tG/fXmpZhw4dcOvWLRQWFsrdLz8/H9nZ2VJ/ZQnRaJAyghAACICFJxLAL8nLspQN55+WKIQA4X0IO/4PvQ8w7PtAYS/RD1Mxfk/JghAwfL9GoRTF4EVhWloanJ2dpZY5Ozvj69evSE9Pl7vf8uXLYWtrK/4rS2Ub+AKChScSoKobTM3Kw42kDK3YpE+iH6ZiXexTpbdPy87HhvPPtGiRfqD3gcJ2RL5NFQzVr1EosjB4UQgUn7kjipgrmtEze/ZsZGVlif9evXqlVRuZxI2kjGJ5NsoSk5CmYWv0izo/IgCwLvaJQeUj0ftAMQTU9W2G5tcoFHkYvCh0cXFBWpp0g3737h1MTExQrlw5ufvxeDxxmYayVq7h3Sf1BCEARPydbFAioDQC2ZDCTvQ+aJ/Lly+jW7ducHNzA4fDwdGjR0vc59KlS6hfvz7MzMxQuXJlbNmyRfuGsphYNcWdofk1CkUeBi8KAwICEBMTI7Xs7NmzaNCgAbhcrp6sYjbJ6Tlq78uBYYkAZfLn5GFIYafSdBQM6T5oE1pZQbtEP0zF9r+T1drX0PwahSIP1tUp/Pz5M549+5anlJSUhLt378LBwQGVKlXC7Nmz8e+//2Lnzp0AhDONN2zYgKlTp2LUqFGIi4vD9u3bsXfvXn1dAqNRNW+sKATfREBAFfkjsWwg+mEqFp/8p1THKI2YYhKl6SgAhnMftEmnTp3QqVMnpbffsmULKlWqhPDwcACAr68vbt26hTVr1qBPnz5aspKdqJv+IMKQ/Jo8aBFvCsBCUXjr1i20atVK/Hnq1KkAgODgYERFRSE1NRUpKSni9V5eXjh9+jSmTJmCjRs3ws3NDb/88gt1mjIoreOUhO0iQDT7urTjAk7WZhqxR5+UtqMAGMZ9YBryKits374dhYWFNBIiQWnSHyRhu1+TBy3iTRHBOlHYsmVLKCqtGBUVVWxZYGAg7ty5o0WrDANNOU6A3SJA3dnXRXGx4aGRl4NGbNIXmugoGHGAjzkFGrKIIqKkygqursVr6+Xn5yM//1uZqbJSaktTYo7Nfk0ep++nYvye4r+PoiLekVeTsaJ3TVqrsYxg8DmFFOVR1nHamXOhqN/IdhGgrDi24gn7VPLuRd5XAetnLWqioyAgwA977tBEfS2gamWFslpqq7wVr9THYLtfk4WwiLfiAZPML4UYt4u237ICFYUUMcr2goc381K4nu0iQFlxvLhHDWwZXA+2FrLDdFkG4EyVvRfDmnqgpAgTTdTXLOpUViiLpbaiH6Zi2oG7CrfhALCzUNzZZbtfK4qqRbxpMfqyARWFFDGNvBzgYiNfGHIAuNqaYULrqtgYVNdgRYCy4tjF1hzt/FxgZmIsc73oytl6HwDl74W7vYXCHxfJRH2KZlCnskJZK7WlzJuZRG5sRe+aBu3XJFEnLYQWoy8bUFFIEROTkIa8r3yZ60R+MrSbH4yNOLC35BmsCFBWHDfycsCNpAyFZWvYfB8A4b1wtTWTO4IiuhcOSobnDDVRXxN8/vwZd+/exd27dwF8q6wgmjg3e/ZsDB06VLz92LFj8fLlS0ydOhWJiYmIiIjA9u3bMX36dH2YzziUzQ12sTUTv9/YkP2aJOqmhdBi9IYPFYUUAN961JlfZL8P2s6CK/VieGV/3NkoAlQRx4Z8H0QMaFhJ5g+r5L1QJKIlMcREfU1x69Yt1K1bF3Xr1gUgrKxQt25dLFiwAADkVla4ePEi6tSpg8WLF9PKChIoK3zW9K1dJvyaJOoW8QYMY6SUIh/WzT6maB5letQ8EyO083MRf1b2x51tIqCkUjR2Flwsl5iJZ6j3AZBdpkISF1szhHbzQ0d/V/AFBK62ZkjLypMrIF3+G12lyIZWVtAsygq39JxvoWVDbs8iSlPEG6D1Gg0dKgopSvWo07LzpRyBKKxoSCJAHXFsiPcBKFkcT2lbTap+mbERB6Hd/DBu1x1wgGL7EQDzu/iWKedK0S/qCDxDbc8iNFWLlu0jpfKg9Rpp+JgC9UImIhEAFC/JUjTEyhZUEcciFN0HgJ1iqCRxzAGw72bxWasd/V2xeXA9uNjK/jFefCqR5iNRdIay+bCSAs8Q27MkmqpFy+aRUnmcvp+KsbvuFLs/onqN9ZfElAn/RUUhRe2QiTwRYGvOxeS21aRG1NiAuvlEhiaGSvrhUJRs39HfFfO7+MncLy0rj/UleijsQd2Oq6G1Z0k0McJH6zWy87tXFioKKWr1qEV09HfFXz+1xpS21WFnLiyDIepZfbfyPKsaUGnyiQxJDJUm2Z4vIFh8SnZ4yhBK9FDYRTs/F0xuWx225tIleiRnHMvCkNqzJJoY4aP1Gg27XiMVhZRSh4JjEtIQHvsEmbnSM5fZ5jxLI44NSQyVRhyXZpSRwkz4AoK45x9w7O6/iHv+gRXPMCD8sf9u5Xmsk/BNduZcTGlbDX/91Frha9sMqT1L8jEnX2EdRpGP2zCA1muUh6HXa6SikAJAfsikpB61ovwztjnP0ohjQxJDpRHHZaWkR1lBJKwG/nYNk/bdxcDfrrEiAiCaKFW0TWblFiI89mmJr580pPYsIvphKn5QYkQstJsfylnTeo2KMOR6jVQUUgAIxZ2tuSlmdvDG/C6+WPd9Hewd1aTEHrWhOU91xbEhiaHSiOOyUNKjrCBPWDE9AqCJjqohtWdAucoKRhxgY5DQxxna9cujNPazZbBDVWhJGorMafiu/9WgK2mWnaE5D0lxnJFTAAcrHlxsSq5VZWhiSCSOiz4XkrUJZWHoJT3KCiUJKw6EP4rt/FwYNxNXlY6qvFp7htaelRkRExDA3tIUgOFdvzyS03PU3tdQ6zVSUVjGkVePTjQaoGh0DDAs51EacWxoYkhdcayoXiFbSxWVRTQhrPSFJjqqhtaeVb0nhnb9soh+mIp1sU9LdQy2DHaoAg0fl2E0EWYpTf4ZkyhtqMyQ6jZK5pFNOXAPi08lYlX0I2TlFihlv7oheApzYHMEQBMdVUNqz4Dq98TQ6zVqqog3GwY7VIWKwjKMJvIBDcF5amqyjCGIIU3lkYlKFe0d1QQ/D1AuP5XCHNgcAdBUR9UQ2rMIde6JIddr1EQRb0Os1wjQ8HGZRlOjAermnzEFTYbKOvq7op2fCyvfnanpPDJjIw4CqpQTv0v05P03rLofZRk2hw81mcLA5vYsibr3pKO/KwQCYPye4oWdlU0xYiKaGOEW1WvcbMS+61eE2qLw1atX4HA4qFixIgDgxo0b2LNnD/z8/DB69GiNGUjRHpocDWCz89R0qIytYkgbeWSK8jQNyZEaGmzPDdVkR5Wt7VkSUY7w8GaeOHr3DTIkRrgU3ZOS6jUyecKRIpT97ZvUphrWn3+qsDwPG69fEWqLwqCgIIwePRpDhgxBWloa2rVrhxo1amDXrl1IS0vDggULNGknRQtoejSArc5TG6EyNoohTYvj0k5iougXNkcA1J0oJQ82tmcRsmx3sOSiV50KaOvnovCesHnCkSIaeTnAxcYMadmyr03yt0/Zeo1sun5FqC0KHz58iEaNGgEADhw4AH9/f/z99984e/Ysxo4dWyZFoUgMsWWkTBujAWx0npoWx2wVQ5oUx2wuaUL5BhsjAKWpIiDveGxsz4B82z/mFCLi72Q0LOG7ZPOEI0XEJKQh7ytf5jrJ3770z/lKHY9t168ItSeaFBYWgsfjAQBiY2PRvXt3AICPjw9SU9mZfFoa2Fr5X5PJ1GwtdqvJyTJsfsOLJmeSG1pR87KMKALQo04FBFQpx3hBqEkfxOb2rAnb2TzhSB6iZyTzS6HM9XYWXPFvnyFef0moLQpr1KiBLVu24MqVK4iJiUHHjh0BAG/evEG5coYxjKosbBVDIjQxU5TNzhPQnDhmsxjSpDg21BGGsg6T34OsDR/E5vasCdsNpeSYCGXe7MIzMUI7PxcAhnf9yqB2+HjlypXo1asXVq9ejeDgYNSuXRsAcPz4cXFYuSzA9jBZ0ZB311puatlpCLknmgiVsV0MaSqPrCz2sA0dpqeGaMMHsbk9a8J2tk84KooypWjSsvPFz4ii68d/nwc0dNeWuXpBbVHYsmVLpKenIzs7G/b29uLlo0ePhoWFhUaMU8SmTZuwevVqpKamokaNGggPD0fz5s1lbnvx4kW0atWq2PLExET4+PiUyg42iyFNOnk2O09Ac+LYEMSQJsQxm0uaUIrDhrw6bfggNrdnTdnO5glHRVHnGZF3/SLWxT7FvpuvWHcv5FGqOoWEENy+fRvPnz9HUFAQrK2tYWpqqnVRuH//fkyePBmbNm1Cs2bNsHXrVnTq1AkJCQmoVKmS3P0eP34MGxsb8WdHR8dS28JWMaRpJ89m56lJcWwoYkiUR1aa/Q1phKEsw5ZoiDZ8EJvbsyZtL9pRLG/JAzhA+ud8xD3/wPjJRyLUfUZE17/h/DOsi31SbHsmdY5Ki9o5hS9fvkTNmjXRo0cP/PDDD3j//j0AYNWqVZg+fbrGDJTF2rVrERISgpEjR8LX1xfh4eFwd3fH5s2bFe7n5OQEFxcX8Z+xsXGpbWGjGNJG7g1bcy80nQ/K9je8aDJnzJDeCFGWYUtenTZ8EJvbs6ZtF3UUeSZGmH7wHgZtu86qSZVA6Z+RfTdTZC5nQ968sqgtCidNmoQGDRrg48ePMDc3Fy/v1asXzp07pxHjZFFQUIDbt2+jffv2Usvbt2+Pq1evKty3bt26cHV1RZs2bXDhwgWF2+bn5yM7O1vqTxZsFEPacPJsdJ7amhzDVjGkjRn09HV3qrFp0yZ4eXnBzMwM9evXx5UrV+Rue/HiRXA4nGJ/jx490qhNbImGaMsHsbU9A5q3ne2TKgFgQMNKckdOAfnPCFs6R6VF7fDxX3/9hb///humpqZSyz08PPDvv/+W2jB5pKeng8/nw9nZWWq5s7Mz0tLSZO7j6uqKX3/9FfXr10d+fj5+//13tGnTBhcvXkSLFi1k7rN8+XIsXLiwRHvYGCbTlpNnW+6JNvNB2VbfTZs5Y6UNRZcVmJQWIwmboiHa8kFsa88iNFnEmy1pBPKQlSYkSUnPCFs6R6VFbVEoEAjA5xcv/vj69WtYW1uXyihl4HCkHzpCSLFlIry9veHt7S3+HBAQgFevXmHNmjVyReHs2bMxdepU8efs7Gy4u8ueZcQ2MaRNJ88m56ntRs4WMaRLZ8+2Au+6RDItBgDCw8Nx5swZbN68GcuXL5e7n5OTE+zs7LRmF9vy6rTlgyTbMxueY00X8Wb7pEpZnV4RU9pWw4TW1RTeFzZ1jkqD2qKwXbt2CA8Px6+//gpAKNI+f/6M0NBQdO7cWWMGFqV8+fIwNjYuNir47t27YqOHimjSpAl27doldz2PxxMX51YGNokhbTt5toghXTVypv+A6MrZM72kiT4RpcXMmjVLarmyaTF5eXnw8/PDvHnzZFZaEJGfn4/8/G9vaZCXFiMJm6IhmqoioAg2PMfaGPln60hZSbUJOQD23XyFCa2rKTwO2zpH6qJ2TuG6detw6dIl+Pn5IS8vD0FBQfD09MS///6LlStXatJGKUxNTVG/fn3ExMRILY+JiUHTpk2VPk58fDxcXTXbgNlS+V9X+X9MLnQL6CYflA1vutGFszeEXCRtUpq0mEOHDuHw4cPw9vZGmzZtcPnyZbnnWb58OWxtbcV/8qIfRWFDXp0u2hobnmNt5UqzdaRMU7mAbMybVwe1Rwrd3Nxw9+5d7N27F3fu3IFAIEBISAgGDRokNfFEG0ydOhVDhgxBgwYNEBAQgF9//RUpKSkYO3YsAGHo999//8XOnTsBCMMwnp6eqFGjBgoKCrBr1y4cOnQIhw4d0qqdTEbbIW829Ka1PQLChtpugPadPdtzkXQJk9JiisLkaIgu2hpbnmNtjfyzdaRMk51eeb+btuZcDG/mKX4TCpspVZ1Cc3NzjBgxAiNGjNCUPUrx/fff48OHD1i0aBFSU1Ph7++P06dPw8PDAwCQmpqKlJRvU8cLCgowffp0/PvvvzA3N0eNGjVw6tQprYW5mR4uFKEtJ88WMQRoTxyz5QcE0L6zZ3MuEgDw+Xw8ePAAHh4eUoX6NQlT02KKwsTUEF21NbY8x9oa+WdTGoEkmu70StYsjPw7CZm5hcjMLTSYItZqi0LRKJw8hg4dqu6hlWL8+PEYP368zHVRUVFSn2fOnImZM2dq1R4RbBghk0TTTp5NYkiENsQxW35AAO07e7blIk2ePBk1a9ZESEgI+Hw+AgMDcfXqVVhYWODkyZNo2bKlxs8pmRbTq1cv8fKYmBj06NFD6eNoIy2G6eiqrbHlOdb2REI2TaoEtNPpjUlIQ3jsE1YMfKiK2qJw0qRJUp8LCwvx5csX8RtNtC0KmQibRsi0BZvEkCSaFsds+QERoU1nz7ZcpIMHD2Lw4MEAgBMnTiApKQmPHj3Czp07MXfuXPz9999aOS+b0mKYFA3RVVtjy3Os7ZF/JqcRyELTnV42Dnyogtqi8OPHj8WWPX36FOPGjcOMGTNKZRQbYduDoi2nzjYxpC3Y8gMiibacPdtykdLT0+HiIswNOn36NPr164fq1asjJCQEv/zyi9bOy/S0GBFMi4boqq2x5TnWRZhX1IkW/Y6cvP+G0eJQk51etg58KEupcgqLUq1aNaxYsQKDBw/WeFV9psOmB0WbTp1tYkhb4pgtPyBF0UbOGNtykZydnZGQkABXV1dER0dj06ZNAIAvX75o5NWYimBqWowIJkZDdNXW2PQc6yLMy7TOQUloqtNr6AMfGhWFAGBsbIw3b95o+rCMhy0PiradOpvEkDadGpt+QHQBm3KRhg8fjv79+8PV1RUcDgft2rUDAFy/fh0+Pj56tk5/MDUaosu2xqbnWJthXiZ2DhShyfqVbBv4UBW1ReHx48elPhNCkJqaig0bNqBZs2alNoxtsOFB0YVTZ4sY0oVTY9MPiC5yxNiSixQWFgZ/f3+8evUK/fr1E8/WNTY2LlZcuizB5GiILtsaW55jQDsj/0ztHMhD051/Ng18qIPaorBnz55SnzkcDhwdHdG6dWv873//K61drIMND4qunDrTxZAunRobfkB0GQZiYkkTWfTt27fYsuDgYD1YwhyYHg3RZVtj+nOszU4ekzsHRdFG558tAx/qUqp3H1O+wYYHRZdOncliSNdOjck/IGwLA2kLVSaQTJw4UYuWMBc2REOY3NZ0hbY7eUzvHIjQZuef6QMfpUHjOYVlGaY/KLp26kx10GxxatpGn2EgJpU0AYSv7VQGDodTZkUhk6Mh+nqemPYc66KTx4bOAaD9zj+TBz5Kg0qiUPL1SCWxdu1alY0xBJj8oDDZqesStjg1baOvMBATZy0mJSXp5bxsgqnREH09T0x7jnXVyWPL74guOv9MHfgoDSqJwvj4eKW2k/euzrICUx8Upjp1XaNPp8akkQV9jJjScDW7YVo0RF/PExOfY1118tjyO6LLzj+T/HppUUkUXrhwQVt2UHSEvpw6kxqNvpwa00YWdD1iyqZZi69fv8bx48eRkpKCgoICqXVlNQoiginREH09T0x9jnWdM86kzoEsdNX5Z5pfLy00p1CLMEkISaJrp87ERqNrp8bEkQVdj5iyZdbiuXPn0L17d3h5eeHx48fw9/dHcnIyCCGoV6+e3uxiEkyIhujreWLqc6zrTh5TOgfy0EXnn4l+vbSUShTevHkTf/zxh8ze9OHDh0tlGNthohCSRFdOncmNRldOjakjC7oeMZU3QmEs4MM1+z08P6bCMzMVjmHHgew04NkzIDYWcNXt8zF79mxMmzYNixYtgrW1NQ4dOgQnJycMGjQIHTt21KktFPnoa8IYUyeq6SMthgmdA0Vos/PPVL9eWtQWhfv27cPQoUPRvn17xMTEoH379nj69CnS0tLQq1cvTdrIOpgshHQJGxqNLpwaU0cWAB2OmBYUoFL6a/i+e4FEp8pSq87/NgYemWmy93v2TOeiMDExEXv37gUAmJiYIDc3F1ZWVli0aBF69OiBcePG6dQeJqPPaIi+JowxdaIaW3L9dI22Ov9M9uulQW1RuGzZMqxbtw4//PADrK2t8fPPP8PLywtjxoyBq46dOJNggxDSFYbaaFSFqSMLIjTmNPPygBcvhEKu6N/Ll6grEGBlpRroMXClVPv418ZJtig0NQXevSvVtamDpaUl8vPzAQBubm54/vw5atSoAQBIT0/XuT1MRd/REH1NGGPy7FuaM67YrtK83q4oTPfr6qK2KHz+/Dm6dOkCAODxeMjJyQGHw8GUKVPQunVrLFy4UGNGsgmmCyFdNl5DbTSqwtSRBUmUHjH9/Bl4/hzw8QH+e/0bAGD9emDSJIDI+pn8hvfntwAgNZJx1aMWssys8NLeFd91bAL/wPpAlSpAhQqAsbF6F1QKmjRpgr///ht+fn7o0qULpk2bhgcPHuDw4cNo0qSJzu1hIkyIhuhrZIzpI3I0Z1w3drHBr6uD2qLQwcEBnz59AgBUqFABDx8+RM2aNZGZmYkvX75ozEC2wWQhpOvGy+RGo0txzOSRBZlkZkqP8j1//u3/af+N6N29C9Su/W0fV1f5gtDGBqhWDahaFbyqVbG5fx0sPPVI/BxuaDpA/Bz6MyCtYu3atfj8+TMA4XuQP3/+jP3796Nq1apKF7k2ZJgUDdHXyBjTZ9+W9ZxxXdjFOr+uJGqLwubNmyMmJgY1a9ZE//79MWnSJJw/fx4xMTFo06aNJm1kFUwVQvpovExtNLoWx4wbWSAESE8Hvn6VztfLzQXc3YEPH0o+xrNn0qLQxwdo3BioWrX4X7lygETt0o4A2vm7MTLcBACVK3/LebSwsMCmTZv0aA3zYFo0RF+zYJk4+1aXnV0mdQ70YRfj/LqGUFkU3r17F3Xq1MGGDRuQlyd0DLNnzwaXy8Vff/2F3r17Y/78+Ro3lC0wUQjpq/EysdHoq2er85EFQoSjerLy+549A7KzgdGjwd+8RepHpImxMeR+Gy4u34Re0bxhf3/g2jWlzWP6rEWKfJgYDdHX88Sk51jXnV2mdQ70YRfTR4zVQWVRWK9ePdStWxcjR45EUFAQAMDIyAgzZ87EzJkzNW4g22CiENJn42VSo9F3z1bjIwsCgVD4ublJL589G/jlF6CENI4P9xLQdeV5qe8l0rE6anlURbnaftKjfVWqAFZW6tnJMoyMjBS+lYnP5+vQGubB1GhIWUYfnV0mdg5UOZ+m7GLiiHFpUFkU/v3334iIiMCsWbMwbdo09O7dGyEhIWjVqpU27GMlTBJCgP4bL1MaDRN6tiqPLHz9CqSkyB7te/ECKCgQhn0lJ33wePIFoZER4OGBdBd37OG4FbsfI7rOAoAyUzZJFkeOHJH6XFhYiPj4eOzYsaPMTqCThEnREKbMetWnHfrq7DK1c6APu5g0YlxaVBaFAQEBCAgIwC+//IIDBw4gMjISbdu2haenJ0aMGIHg4GBUrFhRG7ayCqYIIYAZjZcJjUbf4lguBQVC8Wdh8W1ZYiLQoweQlCRcp4jkZMDb+9tnHx+genXpUT7R/z09wTfholuREUIRus4FYsqPuiQ9evQotqxv376oUaMG9u/fj5CQED1YxRyYEg1hyqxXfduhr84ukzoHTLGLif5MVdSeaGJubo7g4GAEBwfj+fPniIyMxNatWxEWFoZ27drh9OnTmrSTlTBBCAHMbby6Rq/iODdXfg2/lBQgPBz48cdv25crBzx9Kv94ZmbfxJ5AIL1uwADhnxxuPP+g9xFTQP8/pqrSuHFjjBo1St9mMAJ9R0OYMuuVCXboq7PLlM4BU+ximz+Th0befVylShXMmjUL7u7umDNnDs6cOaOJw1I0BFMbr67RujjOz5cO4wLA6NHA6dPAv/8q3FXw9CmMJBc4Ogonczg5yZ7R6+YmDAWrARNGTJnwY6oKubm5WL9+PY2CSKCvaIi+c4OZZoc+O7v67hwwxS62+TNFlFoUXrp0CRERETh06BCMjY3Rv39/nYRXNm3ahNWrVyM1NRU1atRAeHg4mjdvrtDOqVOn4p9//oGbmxtmzpyJsWPHat1OpsCUxqvP4XWNiOOPH6Xr9kn+2dsLw75Ft1cgCLN5lki2d8WVJ7mo8jD12/fA4Qj3UzDhQV30nU7AlB9Tedjb20tNNCGE4NOnT7CwsMCuXbu0em62+TV9REOYkBvMJDv0HQliUqqUPuxiuj9TFbVE4atXrxAVFYWoqCgkJSWhadOmWL9+Pfr37w9LS0tN21iM/fv3Y/Lkydi0aROaNWuGrVu3olOnTkhISEClSpWKbZ+UlITOnTtj1KhR2LVrF/7++2+MHz8ejo6O6NOnj9btBZiRa6DvxsuE4fUSxXENF2E4VnIU7vx54YzeZ8+AjAz5B//4EeDzpd/CUbWqcNTvv1DvUxtnbEwBku3dkGzvikwza4DDEYrSoj1KLQhCQP8/Ikz5MZXHunXrpEShkZERHB0d0bhxY9jb22vtvGz0a/qACSPdTLKDCZEgpqRKFaWsv9teHTiElPBeqiK0a9cOFy5cgKOjI4YOHYoRI0bAWzLJXQc0btwY9erVw+bNm8XLfH190bNnTyxfvrzY9j/99BOOHz+ORIlRnLFjx+LevXuIi4tT6pzZ2dmwtbVFVlYWbGxsVLKXCWJI38gbXhe5KZ0OrxMC/r9vkHjlDgofP4Hj29dw+/AGRs//G/E7cgRo3frb9ufPAyUVZHd1FQrAo0cBBwkxJSES+QKC7+RM8AC+ibG/fmqtkyT9cbvuAJD9I6LN7+PY3X8xad/dErf7eUAd9KhTQaljlqZ9MgW2+TVJdNnpjXv+AQN/K7km5t5RTbT6I8wUO0TQ3xn9oA1/JkIffk3lkUJzc3McOnQIXbt2hbEe3ktaUFCA27dvY9asWVLL27dvj6tXr8rcJy4uDu3bt5da1qFDB2zfvh2FhYXgcrnF9snPz0d+fr74c3Z2tlr2GlKugbowZnh94EDgn3+A589h/OUL/OVt9/y5tCisWlU4aufuXnw2r+izvBFyiTbCpB6lPtMJ9B2+lsX9+/eV3rZWrVoaP7/e/ZqPT8k5qvXqAcePSy/r3h15128hO68QngICz/8WfzDiwMaMCzPuf8ecOlX4J+LTJ8DXV/H5RBw7BtSvL/7Y6J+ruLF5BPgC+eMZxkYcOB4tBzx6JL1ixgxg796Sz9mlC7B1q/SyBg2+veYRQBMANz7lF7NjeavhOO7X8tuIe8F7oGJtKMXNm9KF4X/9FVi0qOT9qldHx/PnpSJBTUMnofzta+BsLGHfUaOA0FDpZcrmzu7aBbRsKf7IP38BX4MGQUAIjDgcmJoYyS+G//q19OeFC4Hffiv5nIGBwO7d0statwaePBF/JAAKvgqK27FggTDPW0RqKtCwYcnnBIBz56SrPOzZA8yciY5fBYjLKZC723sre3QPDpf2Z2PGAKdOlXzO3r2Vs02DqCwKjxd1CjomPT0dfD4fzs7OUsudnZ2RJtFgJUlLS5O5/devX5Geng7Xom9nALB8+fJS1yRjjBjSM1oTQ1+/Ai9fys7vq19f6LAkiY8HHj+WfzwjI8DTs/hyd3dh3T+z0okUpoSbROgrnUDf4WtZ1KlTBxwOB6LAia6LV+vdr6Wmlmyku3uxRZkv38DuXSpktgzJfnTRTjUhJU6+ElMg/YNrnJ8Hp+z0kvcj+cWXlZDjK0ZWmkhamtS+HABOMnY1L8yXDtsKMpS/1qLP1ufPyu1rawugSLg075Ny+2ZlFV+mrL0SHYzoh6mI/v06wt8q8SzJs0OZ86bL+O7fvi323fCKbyW8n5Lw+cpfa9HSYF++AP/+Cx6AkrrQrkX9WYaSz0RmpnK2aRCNzD7WB0WdNiFEoSOXtb2s5SJmz56NqRI92+zsbLjLcIqKYNLIkD5zGjUqhg4eBLZvFwq/5GT5NfxkCbiqVYVlYby8ZM/o9fAATE2L78fhlFoQAswcIdNHLhATcqCKkpSUJP5/fHw8pk+fjhkzZiAgIACAcFTuf//7H1atWqVVO/Tm11xdSx4pdHSU+sgXEDwoMEVVK/nPj7ERB47WPHCKhr44HKCCkqG0om3S3ByoUAF5hQJk5xVKjdQZS45QynoDj729cud1kNEhcXGRuWlRO3K5POkR98fZyl9r0eiblZVy+xbpHAAAypdXbt//BKUUytr7X7UFUUSscT5Bqoznwd7C9NuosSI7lDlv+fLFlzk7A1lZyCsU4OMX+aN2H7L40hEiY2Plr9WkiFyysBDvq+i8763si/szBwflzmtnp5xtGoR1orB8+fIwNjYu1nt+9+5dsV6zCBcXF5nbm5iYoFw52Q6Nx+OBV7S8iIowZWRI37kmJYkcs8I8VMpMg/e1DCD2rfSI340bwrIsIlJTgehoxSc0MyteGgYAfv8dfEsr3HiVrRdxzMQRMn3BlNnwIjw8PMT/79evH3755Rd07txZvKxWrVpwd3fH/Pnz0bNnT42fX+9+7dEjQMWcpRtJGRjSY26J28nMqbO2Lh4+VJauXYHXr2EGgKtqZ3f1auGfOty6JXNxUTsGWpthnaQd3t7qX+vo0dLhTjnwBQQ3nn+Qvg9FQ6yqoIK9khGxa5VqIeCHHVLrlc6VDg0tHsZWlvPnwRcQtCopZ9vMDH8JyDc7XF3V/26CgoR/ED4D91T5nS2amiCP7Gxg/Xr17FMT1olCU1NT1K9fHzExMejVq5d4eUxMjMw3EQDCt7CcOHFCatnZs2fRoEEDmXk3moIJI0NMyGksKoZs8j5jzoUIeH58A4+PqXD9/EG4YYSMnZ89kxaFVasK/7WyKj7SJ8r1k1PDL/rfPCw8cUdv4piJI2T6RN+z4eXx4MEDeHl5FVvu5eWFhIQErZyTTX5NBBM6vUyZ9apPO/Td6WdKREzfdjDVn6kK60QhAEydOhVDhgxBgwYNEBAQgF9//RUpKSni+lyzZ8/Gv//+i507dwIQzsjbsGEDpk6dilGjRiEuLg7bt2/HXmUSjkuBvkeGdJ7TmJEhs4afcZ8+CO02UCyG8kx46H8/BkYyLZPAzq54bk/LlsLcHicnlUq2MEEcA8wZIWNCiSSAOT/qkvj6+mLJkiXYvn07zP5LG8jPz8eSJUvgq+zkCDVgi18Toc9OL1OeX33DBL/GhM4BU+xgoj9TFZVEoSqTTLp3766yMcry/fff48OHD1i0aBFSU1Ph7++P06dPi0NAqampSElJEW/v5eWF06dPY8qUKdi4cSPc3Nzwyy+/aL2Wl75HhrTec9qxAzhz5psA/PhR9nZeXug4daqEGALe2DiiYvY7ZFjagVO1Cuxr+RUf+ZOV12NuLvxTAaZN+NF3j1LfIwtMZ8uWLejWrRvc3d1Ru7Zw1ui9e/fA4XBw8uRJrZ2XLX5NhL46vUx+fnUpVpni15gQEWOSHWxHpTqFRkq+VovD4Whlhp4+YWOdQrXqJwkEwrw9ydG+58+BDx+EU/IlGTNGWDKhJLp0Af77MRU5zZyHCbDxqIj6tTy1LoaYVk9MnzCqXqQG0XQ9ry9fvmDXrl149OgRCCHw8/NDUFCQTorz65LS3jdd17tk8vOraz/PFL8mqr9aUudA2/VXmWKHyBZNdA4YX6dQIBBoyw6DRl8jQ8r0iCpmpqHhxuVA+r/fBGBuruyNs7Olk9FF+X0cDlCpkuwafpUrS9XwEw+vV5H/6i5Nw4SwAhNgysiCPNuYFA60sLDAaCUS/Ms6ukyHYPLzq48wLlP8mr4jYkyzg8kj2crAypxCNqLzXIPCQjTiZ6DX2/uwef0SHh9TUSkzFTvqd8MVr3oAhA2lMvcr3LaWVN0Uwqn7KSmAv8SE/iFDgG7dhCVeSjlTW5vQsIIQfSdiy4MJTvT48ePo1KkTuFxuiWky2kyNYSO66vQy9fnVl1hlkl9jSq60vu1gQo5naSmVKMzJycGlS5eQkpKCgiIFRidOnFgqwygqsm2bsDizaKJHcjKM+XysK7LZ7Yp+uOJVT9xzGjK4NbDhvw+mpsKRPVk1/CpVAorOaHRxkVu7i0noe8KPInQ5QsaUkQVJmOJEe/bsibS0NDg5OSksOWOIqTGaQBedXiY+v4D+xCrT/Jq+c6X1bQeTR7JVQW1RGB8fj86dO+PLly/IycmBg4MD0tPTYWFhAScnJyoKNUVOjrDgsmSOn5UV8L//SW8XEQEo8b5T98y3AL71nNr5uwIXLghH+ypWLF48VUvoUgwxJaxQFF2PkDFpZAFglhOVTI2haTLqo812zbTnV4S+xCoT/RpTZt/qww6mjmSritqicMqUKejWrRs2b94MOzs7XLt2DVwuF4MHD8akSZM0aaNBodBp/vOP8N2ikgLwzZviB3F3Ly4Kq1b9JgqtrIBq1aTq9/ErV8Fd0/KwNLfFXlsL6fNKvLtSF+gjXKjvsEJR9DFCxrSRBTY50czMTNjp4e0CbELb7Zppz68IfYpVpvk1fWMwb+7SI2qLwrt372Lr1q0wNjaGsbEx8vPzUblyZaxatQrBwcHorYcXOTOajAzEnbmG6KN/wfZNCjw+vsGM5oPBr+TxrfHevQvMmVPysV6/BvLypF+9Nm0aMHasUAQ6Ohar4WcMoP5/f/pEn+FCpoQ39DVCxrSRBaY60ZUrV8LT0xPff/89AOEbTg4dOgRXV1ecPn1aXKaG8g1dtGumPb8i9C1WmeLXJNGHONN3bjJTR7JVRW1RyOVyxe/XdHZ2RkpKCnx9fWFraytVS6vMwecDu3cXK+CMjx8RACBAYtOTvi1w0db5m9MUzeYV4eQk/60dRd/Fy4IfKiaEC5kQ3tDnCBmTRhaY6kS3bt2KXbt2ARC+USQ2NhbR0dE4cOAAZsyYgbNnz+rUHqajy3bNpOdXBBPEKhP8mgh9iDMm5Cbru3OgKdQWhXXr1sWtW7dQvXp1tGrVCgsWLEB6ejp+//131KxZU5M2sgsjI2DCBODTpxI39fz4Rtppjm8I4wMHvok/HdUl0hVsChdqE32PkDFlZIGpTjQ1NRXu7u4AgJMnT6J///5o3749PD090bhxY53awgZ03a6Z8vwWtUkfYpVppZz0Ic6YMNgAMKNzoAnUFoXLli3Dp/+Ez+LFixEcHIxx48ahatWqiIyM1JiBrIPDEYq6+Hjx5zy3irhl4oCX9q5ItnMT/mvvipd2wsYhdprphQjo109jpjDNYehbDDEFJoyQMWFkgalO1N7eHq9evYK7uzuio6OxZMkSAAAhhM48loE+2jUTnt+i6Fqs6jtcWhR9iTMmDTYwcSRbVdQWhQ0aNBD/39HREadPn9aIQQbB4sUAIUJx6OWFM4npSr1ZRJNOk2kOA9CfGGKaOGbqCJk+YKIT7d27N4KCglCtWjV8+PABnTp1AiDMo65aNMWDorN2zbR2LAtdiVUmhEuLoi9xxrTBBiaOZKsCLV6tDbp0kfqoazHERIcB6EcMMVEcM3WETF8wzYmuW7cOnp6eePXqFVatWgUrKysAwrDy+PHj9WITk9FFu2ZiO1aENgUsU8KlRdGXOGNC5KUoTBzJVha1RaGXl5d4ooksXrx4oe6hDQ5diiGmOgxA92KIqeIYoDlIRWGSE+VyuZg+fXqx5ZMnT9a9MSxA2+2aye1YFtoWsEwKl0qiL3FGIy+aRW1RWNRBFhYWIj4+HtHR0ZgxY0Zp7TIodCmGmOowROhKDDFZHIso6zlITOb333/H1q1b8eLFC8TFxcHDwwPh4eHw8vJCjx499G0e49BWu2ZDO5ZEFwKWaeFSEfoSZ0yOvDC1E64ItUWhvALVGzduxK1bt9Q2yFDRlRhiqsOQRBdiiOniWERZzkFiKps3b8aCBQswefJkLF26VDy5xM7ODuHh4VQUykEb7Zot7RjQnYBlYrgU0K84Y2JuMls74RrPKezUqRNmz55dtmcgy0EXYoipDqMo2hZDbBDHuoJNoy1M6FmvX78ev/32G3r27IkVK1aIlzdo0EBmWJnyDVG7Fn2PJ++/KdX3yKZ2rCsBy+RwqT7FGZNyk9ncCde4KDx48CAcHGjsXh7aFkNMdhi6hC3iWIQ2xRBbRluY0rNOSkpC3bp1iy3n8XjIycnRmR1sRZPfI5vasa4ELJPDpYB+xRkTcpPZ1AmXRamKV0tONCGEIC0tDe/fv8emTZs0YhxFdZjuMIqiLTHEJnGsbTHEhtEWJvWsvby8cPfuXXh4eEgt//PPP+Hr66sTG9iKpr9HNrVjXQpYJoZLJWGCONMXbOmEy0NtUdijRw8pUWhkZARHR0e0bNkSPj4+GjGOoh5MdxgitCmG2CKOdSGGmD7awrSe9YwZM/DDDz8gLy8PhBDcuHEDe/fuxbJly7B9+3atn5+taON7ZEs7BnQvYJkULpWHrtJBmJB2IoINnXBFqC0Kw8LCNGhG2UPbDzHTHYYuxBDTxbGuxBDTR1uY1rMePnw4vn79ipkzZ+LLly8ICgpChQoVsH79ejRv3lzr52cr2voemd6ORehSwBb9/ehay40xvl2ErtJBmJJ2IoLpnfCSUFsUGhsbIzU1FU5OTlLLP3z4ACcnJ/o6KAXo6iFm6hC+LkeGmCyOdSWGmD7awsSe9ahRozBq1Cikp6dDIBCAz+dj2bJl+OGHH5Cbm6szO9iEtr5HvoDA1twUMzt4IyOnAA5WPLjYMKcdS6ILAcs0ESQLXaWDMCntRATTO+ElYaTujoTIulwgPz8fpqamahtk6Ige4qJiQPQQRz9M1ZNlukMVMaQJROK4R50KCKhSjjE/JLoUQ6IfKxdb6d6pi62Z3mfCMaVnnZmZiUGDBsHR0RFubm745Zdf4ODggI0bN6Jq1aq4du0aIiIitGoDm9HG9xj9MBXfrTyPgb9dw5QD97D4VCJWRT9CVm4BY9pxUTr6u+Kvn1pj76gm+HlAHewd1QR//dRaoyKIyb8fJXX6AWGnny+QrSGYdh5VEXXCgW+dbhFM6ISXhMojhb/88gsAgMPhYNu2beJXQAEAn8/H5cuXaU6hHHQ1Qsak/ApZMHFkSB/oWgwxddSUKT3rOXPm4PLlywgODkZ0dDSmTJmC6Oho5OXl4fTp0wgMDNTauT9+/IiJEyfi+PHjAIDu3btj/fr1sLOzk7vPsGHDsGPHDqlljRs3xrVr17RmpyI0/T0ycRRIWbQRpWFa7q08dBUBYVraiSRsSXmQhcqicN26dQCEI4VbtmyBsbGxeJ2pqSk8PT2xZcsWzVloQOjiIWZDaEFXYojp4lgfYoiJKQVMCW+fOnUKkZGRaNu2LcaPH4+qVauievXqCA8P1+p5ASAoKAivX79GdHQ0AGD06NEYMmQITpw4oXC/jh07StWE1WeURpPfI1sEUElo0gcxWQRJoqtOP9MHF5jaCS8JlUVhUlISAKBVq1Y4fPgw7O3tNW6UoaLth5gtPWtdiCE2iGNdiSGmi2OAGT3rN2/ewM9PGPapXLkyzMzMMHLkSK2fNzExEdHR0bh27RoaN24MAPjtt98QEBCAx48fw9vbW+6+PB4PLi4uWrdRWTT1PbJFAClC0z6I6SJIhK46/UxJO1EEEzvhJaH2RJMLFy5o0g6lYXOYRZsPMZt61toWQ2wRx4D2xRAbxLEIffesBQIBuFyu+LOxsTEsLS21ft64uDjY2tqKBSEANGnSBLa2trh69apCUXjx4kU4OTnBzs4OgYGBWLp0abHJf5Lk5+cjPz9f/Dk7O1szFyGB5PeYlpUrnhxia24KvoAo9X2yRQDJQxs+iA0iCNBdBIQpaSeGhtqisG/fvmjQoAFmzZoltXz16tW4ceMG/vjjj1IbJws2h1m0+RCzrWetLTHEJnEsQltiiE3iWIQ+e9aEEAwbNgw8Hg8AkJeXh7FjxxYThocPH9boedPS0mQKOScnJ6Slpcndr1OnTujXrx88PDyQlJSE+fPno3Xr1rh9+7b4GoqyfPlyLFy4UGO2y8PYiIOs3AKsOvNYrQ4JWwSQLLTlg9gignQVAWFK2okysCFaI0JtUXjp0iWEhoYWW96xY0esWbOmVEbJg+1hFm0+xGzsWWtDDLFNHIvQtBhioziWRB9ONDg4WOrz4MGDS3W8sLCwEgXYzZs3AUDqRQAiCCEyl4v4/vvvxf/39/dHgwYN4OHhgVOnTqF3794y95k9ezamTp0q/pydnQ13d3eFNqpDaTskbBFAstCWD2KTCNJVOggT0k5Kgk3RGqAUovDz588yR9u4XK5WQhKAYYRZtPUQs7VnrWkxxEZxrA3YKo4B/TlRyUiCJpgwYQIGDBigcBtPT0/cv38fb9++Lbbu/fv3cHZ2Vvp8rq6u8PDwwNOnT+Vuw+Px5I4iagpNdEjYJICKok0fxAYRJEJX6SD6TjtRBBujNWqLQn9/f+zfvx8LFiyQWr5v3z5xsramMZQwizYeYjb3rDUJW8WxCE2NkLFVHLPRicqjfPnyKF++fInbBQQEICsrCzdu3ECjRo0AANevX0dWVhaaNm2q9Pk+fPiAV69ewdVVv/dHUx2Sdn4umNy2OiL/TkJmbqF4ORMFkCTa9kFMFkFF0XY6CJPf7MLWaI3aonD+/Pno06cPnj9/jtatWwMAzp07h71796qcT1gWwyyabixs7lkDmhNDbBbHmhwhY6M4ZqsTLS2+vr7o2LEjRo0aha1btwIQ5kp37dpVKvrh4+OD5cuXo1evXvj8+TPCwsLQp08fuLq6Ijk5GXPmzEH58uXRq1cvfV0KAM10SGS1BTtzLoY388SE1tUY/f1rywexKS+tKNqwnelhWbZGa9QWhd27d8fRo0exbNkyHDx4EObm5qhVqxZiY2NVLvJaVsMsgGYbC5tCC5JosnGzVRxreoSMjeKYrU5UE+zevRsTJ05E+/btAQj964YNG6S2efz4MbKysgAIZ0Y/ePAAO3fuRGZmJlxdXdGqVSvs378f1tbWOrdfktJ2SOS1hazcQoTHPoW3izVjfRmgHR/EdAGkCG3YzoaIAlujNWqLQgDo0qULunTpUmz53bt3UadOHaWPU1bDLNpoLGwKLQDaadxsE8faGCFjozhmqxPVBA4ODti1a5fCbSRfLWpubo4zZ85o2yy1KE2HxFBGizXpg9gggOShDdvZ8oywMVoDlOLdx0XJysrCpk2bUK9ePdSvX19Th5VCMsxy7do1XLt2DaNGjZIZZjly5AgA4YSY6dOnIy4uDsnJybh48SK6deum9zCLNt9hydR3/RZFm++u1Ob7RzWNtt4FzeT3HcuCrU6UIo2id78Cwud5fhdfmX5J1+9F1yaSPmhd/9qY38UXMzv6iOs1KgNT3++rDNqynS3PiKhzJO/XlwPhIBCTojVAKUcKAeD8+fPYvn07jhw5Ag8PD/Tp0wfbt2/XhG0yMYQwi7Z6OmzLOdF2uJAt1eS1PVuRLSPHbAx5U2Qjb6RMxOJTiTAy4hTrmBjaaHFp6zWyOaVCW7az5RlhY7QGUFMUvn79GlFRUYiIiEBOTg769++PwsJCHDp0SGszj0UYQphFG42FjTkn2mrcbBPH2h4hY4s4ZqsTpcimo78rBAJg/J47xdbJCx8a2mhxacOnbBFAstCW7Wx6RtiWygSoIQo7d+6Mv/76C127dsX69evRsWNHGBsbY8uWLdqwzyDRdGNha86JNho3G8Uxna34DTY6UYps+AKCxacSZK6TFxFp5OUAFxszpGXL9n1sGi3WRESITQKoKNqynW0RBTZFawA1ROHZs2cxceJEjBs3DtWqVdOGTQaPJhsLW5JuZaHpxs1WcUxnK0rDNidKkY06EZGYhDTkfeXL3J5to8WaiAixTQBJoi3b2RhREEVrRB31k/ffMNavqTzR5MqVK/j06RMaNGiAxo0bY8OGDXj//r02bDNYNJmAypakW1koSkhXtXGzOSEb0OykEG1OYtIVbJksRZGPspGOtKxcAN+e28wvhTK3s7PgMrZjJwtNRISMjTiY38VPrqgCmCeARGjSvxeFbZPoAOHz/d3K8xj42zVM2ncXA3+7hu9WnmecP1Z5pDAgIAABAQH4+eefsW/fPkRERGDq1KkQCASIiYmBu7u73utkMR1N9nTYnHMCaC5cyOaEbBGSI2RpWbnIyCmAgxVPPFtRE+KYySPHFMNC2YjI4lOJ4JkYYfGpRJnPrQieiRHa+en3/fWqoImIUPTDVLkheDakVGgrHYQvILA1N8XMDt5iP+liw8yRN4BdUSy1Zx9bWFhgxIgRGDFiBB4/fozt27djxYoVmDVrFtq1a4fjx49r0k6DQ1ONhc05JyI0IYbYLo5FlOXZihTDoqTwoYiPOQUYvye+xOOlZeez6rktbfhUnpAQMb+LL2OEhCI04d8lUZQaw0RByLaOeqlL0gCAt7c3Vq1aheXLl+PEiROIiIjQxGENHk00FjbnnEhSWjFkCOIYKNuzFSmGhWRERBGqJHSw6blVFBHCf58HNJT96lRFQgIQ+vXFpxLRwd+VEUKiJErr30WwacRNBNs66horXg0IawL27NmTjhKqgGRjWXwqEVP2q5ZroM28DV1S2jw4thYKlUQTeZGGIo4phoEoIuJgydXI8dj23MrLfROxLvapTF/P5lxxWWgiz5mteeNs66hrVBRSVEcTjYWNSbeSaKKxG4I41sQPgSGIY4ph0dHfFfO71ijVMdj83IrebDKlbXWZ62X5erYJCUVoSsyxVSizraNORaEe0VRjkUy6nd/FF+u+Z/Zr3Yqiqcbezs8Fk9tWh6259KgEW8SxpmYrsl0cUwwPF5vS/eARsP+53XczReZyWb6ebUJCEZry72wVymzrqGskp5CiHprINWBb0q0sNNHYZd0HO3MuhjfzxITW1VhxLzT1QyASx5F/JyEz91t5DzbMVqQYJqIfRkX+ThEjmnmy+rlV1dcbUhFvTYk5tgplttVVpCOFeqS0jcUQ6tEBpW/s8u5DVm4hwmOfIiYhrdQ26gJN9ChFtbDWxT4RC0I7cy6mtK3GmpFjiuEhOYKtDmwqRSMLVX29IRXx1pSYY9uImyRsSvGiolCPlKaxsDXpVhalaeyGdB9KG/o1FHFMMUw6+rsipJmnyvsx9YdeFZT19cnpXwyuiLcmxdyAhpVYWcgb+JZbundUE/w8gLkpXlQU6pHSNBa2Jt3KojRiyJDuAyC/R2lrzsXkttXkjpgYkjimGC5t1RjxY/IPvbKU5OtFrIt9glmHHxhUEW9F/h1QXJpHhGQERBZMHHGTBRve1ERFoR4pjRhia9KtPNQVQ4Z2HwDp2Yp2/02aycwtlFu+AjA8cUwxTETiSBmMOMCmIOb/0CuDyNcr0yWTN0IoQlTEm02oW5oHkB8BEUFTYzQLFYV6Rl0xxNakW0WoI4YM8T4AwpyicIm8QBHy8kUNURxTDA+ROFJmfGTDwLroXMtwfug7+rtiSttqGjkWG9uxOqV5lCnive/mK80bW4ahopABqCOGRLPT5MHkpFtFqCqG2Jx8LA91QsGGKo4phoeoIyxvxNDV1gxbBtdD51puOrZM+3iWt9TIcdjcjlUpzUMjILqHlqRhCCIxpOzrewxpdpoIdd4RaWzEwfwufhi/p/irtNh6H9QpVWQorzuklA3kveLTxUb4jLKpvapCacUc29uxqr6NRkB0Dx0pZACqjgwZ2uw0Eer0CqMfpmLxqQSZ27Ml+bgo6jhCkThm68y8ss7SpUvRtGlTWFhYwM7OTql9CCEICwuDm5sbzM3N0bJlS/zzzz/aNVSDiJLue9WriJDmldGrLnOT7zWFKjmVsmB7EW9VfRuNgOgeKgoZgCpiqKQcC4B9s9NEqOowSkpAnt/Fl3WCEFDPERqiOC5LFBQUoF+/fhg3bpzS+6xatQpr167Fhg0bcPPmTbi4uKBdu3b49OmTFi2llIbS1mtkexFvVX2boaZJMRkqChmAKmKoJAEJsHN2GqCaw1AmAXnxqURWlmBRpnyFgyUX9T3sARiuOC5LLFy4EFOmTEHNmjWV2p4QgvDwcMydOxe9e/eGv78/duzYgS9fvmDPnj1atpZSGtSt1wiwv4i3Mr7NiAN8zCkAYJhpUkyHikIGoIoYMuQcC1UchiEnIJdU1wsAMnIKEbj6Ak7ff2Ow4pgin6SkJKSlpaF9+/biZTweD4GBgbh69aoeLaMogzr1Gg1hREyZkVIBAX7YcwfLTycYZJoU06GikAGoIoYMOcdCFYcRq+TbOdgojoGS63oBwklI4/fEG6w4psgnLU34/Ds7O0std3Z2Fq+TRX5+PrKzs6X+KLpHndxCQxkR6+jvio1BdaHoUgiA364kGWSaFNOhopABqCKGzj9KU9iY2J5joYzDAIB9t5SrTcVGcSyio78rLs1oBQdLU5nrVRn7Y6s4ZjNhYWHgcDgK/27dulWqc3A40g2FEFJsmSTLly+Hra2t+M/dXfGbJCjaQZXcQkMq4i3C3pKHkoIXJa1na5oU06GikCEo33tKLrGxsL1HWZLDIABy8mXnmYhguzgWcfvlR2T8l19TGtgsjtnKhAkTkJiYqPDP399frWO7uAhHSIqOCr57967Y6KEks2fPRlZWlvjv1Sta+FdfdPR3xZbB9WBnwVW4naEV8QY010mlnV3NwzpRaMilG5TpPSnCiANsNIAepaYaOtvFMVD6e2Eo4piNlC9fHj4+Pgr/zMzUE+teXl5wcXFBTEyMeFlBQQEuXbqEpk2byt2Px+PBxsZG6o+iPzr6u+L2vHZSLy4QYchFvDXVSaWdXc3DuuLVotINAQEB2L59u1L7iEo3REVFoXr16liyZAnatWuHx48fw9raWssWK09pBYCAAPZyQo1sQhMNfXLb6qwXx0Dp7wXb65qVFVJSUpCRkYGUlBTw+XzcvXsXAFC1alVYWVkBAHx8fLB8+XL06tULHA4HkydPxrJly1CtWjVUq1YNy5Ytg4WFBYKCgvR4JRRVMTbiYFLbapjQuipuJGXg3ac8OFkbdhFvUU5lSZU05MH2It5MhnWicOHChQCAqKgopbYvWroBAHbs2AFnZ2fs2bMHY8aM0ZapKqMJMWQIw+klvZ1DGTzLW2jUJn1RWufJ9rpmZYUFCxZgx44d4s9169YFAFy4cAEtW7YEADx+/BhZWVnibWbOnInc3FyMHz8eHz9+ROPGjXH27FlGdXQpyiMq5l0WEOVUjt1V/E1UykA7u9qDdeFjVVG3dIM+ZumVtto9YBjD6aUt8AoYxn0ASn8v6Ow8dhAVFQVCSLE/kSAEhB3cYcOGiT9zOByEhYUhNTUVeXl5uHTpkto5ihSKrilNvUba2dUeBi8K1S3doI9ZeqUVAIaUOyYqyVI0z0YZDOk+AMJ7MaVtNZX3M7T7QKFQDAt16jUCtLOrTRghCplYukFfs/TUFQCA4Q2nd/R3xcZB9VTez9DuAwBMaF1N4eueZGGI94FCoRgO6kTHaGdXuzAip3DChAkYMGCAwm08PT3VOrZk6QZX12/DzSWVbuDxeODxeGqds7RMaF0Ne2+8Qlq2cnlkRhxgw0D2zzqWRZPK5ZTOqTPk+2BsxEFYd+VycAz5PlAoFMNB1dxCDmhnV9swYqSQiaUb9IlIAHAg/zVnkhhiHSsRIqdR1u8DULbrmlEoFMNEWb9mT19rpxMYIQpVISUlBXfv3pUq3XD37l18/vxZvI2Pjw+OHDkCAFKlG44cOYKHDx9i2LBhjC/doMxrzgy5jpUkonshL8xQVu4DUHbrmlEoFMNFkV+zM+diSttquDWvHRWEOoBDCClFuWTdM2zYMKnSDSIkSzdwOBxERkaKZ+oRQrBw4UJs3bpVXLph48aNKs3Uy87Ohq2tLbKysnRa8JUvIOLaVeUteQAHSP+cb/B1rGQhuhdpWbnIyCmAgxUPLjZl7z6IkHw2yuLzIIm+2ifbofeNwjSoX/uGPton60ShvsjKyoKdnR1evXpFnSeFwjCys7Ph7u6OzMxM2Nra6tsc1kD9GoXCXPTh1xgx0YQNfPr0CQDoC+QpFAbz6dMnKgpVgPo1CoX56NKv0ZFCJREIBHjz5g2sra0VlrKRh0jxs71HTq+DWRjCdWjiGggh+PTpE9zc3GBkxLpUab2hrF8zhOesKPSa2IGhXZMq16MPv0ZHCpXEyMgIFStWLPVxDOUl9PQ6mIUhXEdpr4GOEKqOqn7NEJ6zotBrYgeGdk3KXo+u/RrtUlMoFAqFQqFQqCikUCgUCoVCoVBRqDN4PB5CQ0P19pYUTUGvg1kYwnUYwjUYOob4HdFrYgeGdk1Mvx460YRCoVAoFAqFQkcKKRQKhUKhUChUFFIoFAqFQqFQQEUhhUKhUCgUCgVUFFIoFAqFQqFQQEWhVvn48SOGDBkCW1tb2NraYsiQIcjMzJS7fWFhIX766SfUrFkTlpaWcHNzw9ChQ/HmzRvdGV0EVa8BAA4fPowOHTqgfPny4HA4uHv3rk5slWTTpk3w8vKCmZkZ6tevjytXrijc/tKlS6hfvz7MzMxQuXJlbNmyRUeWKkaV60hNTUVQUBC8vb1hZGSEyZMn687QElDlOg4fPox27drB0dERNjY2CAgIwJkzZ3RoLUWSpUuXomnTprCwsICdnZ3MbVJSUtCtWzdYWlqifPnymDhxIgoKCnRraCnw9PQEh8OR+ps1a5a+zVIJVX0ekwkLCyv2fbi4uOjbLJW4fPkyunXrBjc3N3A4HBw9elRqPSEEYWFhcHNzg7m5OVq2bIl//vlHP8ZKQEWhFgkKCsLdu3cRHR2N6Oho3L17F0OGDJG7/ZcvX3Dnzh3Mnz8fd+7cweHDh/HkyRN0795dh1ZLo+o1AEBOTg6aNWuGFStW6MhKafbv34/Jkydj7ty5iI+PR/PmzdGpUyekpKTI3D4pKQmdO3dG8+bNER8fjzlz5mDixIk4dOiQji2XRtXryM/Ph6OjI+bOnYvatWvr2Fr5qHodly9fRrt27XD69Gncvn0brVq1Qrdu3RAfH69jyykAUFBQgH79+mHcuHEy1/P5fHTp0gU5OTn466+/sG/fPhw6dAjTpk3TsaWlY9GiRUhNTRX/zZs3T98mKY2qbYwN1KhRQ+r7ePDggb5NUomcnBzUrl0bGzZskLl+1apVWLt2LTZs2ICbN2/CxcUF7dq1E7+PXG8QilZISEggAMi1a9fEy+Li4ggA8ujRI6WPc+PGDQKAvHz5UhtmKqS015CUlEQAkPj4eC1aWZxGjRqRsWPHSi3z8fEhs2bNkrn9zJkziY+Pj9SyMWPGkCZNmmjNRmVQ9TokCQwMJJMmTdKSZapRmusQ4efnRxYuXKhp0ygqEBkZSWxtbYstP336NDEyMiL//vuveNnevXsJj8cjWVlZOrRQfTw8PMi6dev0bYbaaKKNMYnQ0FBSu3ZtfZuhMQCQI0eOiD8LBALi4uJCVqxYIV6Wl5dHbG1tyZYtW/Rg4TfoSKGWiIuLg62tLRo3bixe1qRJE9ja2uLq1atKHycrKwscDkdu2EabaOoadElBQQFu376N9u3bSy1v3769XJvj4uKKbd+hQwfcunULhYWFWrNVEepcBxPRxHUIBAJ8+vQJDg4O2jCRUkri4uLg7+8PNzc38bIOHTogPz8ft2/f1qNlqrFy5UqUK1cOderUwdKlS1kT/jYUX1GUp0+fws3NDV5eXhgwYABevHihb5M0RlJSEtLS0qS+Mx6Ph8DAQL1/ZyZ6PbsBk5aWBicnp2LLnZyckJaWptQx8vLyMGvWLAQFBenlReCauAZdk56eDj6fD2dnZ6nlzs7Ocm1OS0uTuf3Xr1+Rnp4OV1dXrdkrD3Wug4lo4jr+97//IScnB/3799eGiZRSIqv92Nvbw9TUlDXP6qRJk1CvXj3Y29vjxo0bmD17NpKSkrBt2zZ9m1YihuIrJGncuDF27tyJ6tWr4+3bt1iyZAmaNm2Kf/75B+XKldO3eaVG9L3I+s5evnypD5PE0JFCFZGVAFv079atWwAADodTbH9CiMzlRSksLMSAAQMgEAiwadMmVl6DPilqX0k2y9pe1nJdo+p1MBV1r2Pv3r0ICwvD/v37ZXZQKOqhig9QBib6CVWuccqUKQgMDEStWrUwcuRIbNmyBdu3b8eHDx/0Zr+qGIqvAIBOnTqhT58+qFmzJtq2bYtTp04BAHbs2KFnyzQLE78zOlKoIhMmTMCAAQMUbuPp6Yn79+/j7du3xda9f/++WO+gKIWFhejfvz+SkpJw/vx5jY8S6uIa9EX58uVhbGxcrIf87t07uTa7uLjI3N7ExERvvVJ1roOJlOY69u/fj5CQEPzxxx9o27atNs0scyjrA5TBxcUF169fl1r28eNHFBYW6vVZLc01NmnSBADw7Nkzxo9MGYqvUISlpSVq1qyJp0+f6tsUjSCaSZ2WliYViWLCd0ZFoYqUL18e5cuXL3G7gIAAZGVl4caNG2jUqBEA4Pr168jKykLTpk3l7icShE+fPsWFCxe04pC0fQ36xNTUFPXr10dMTAx69eolXh4TE4MePXrI3CcgIAAnTpyQWnb27Fk0aNAAXC5Xq/bKQ53rYCLqXsfevXsxYsQI7N27F126dNGFqWUKZX2AMgQEBGDp0qVITU0V/8CdPXsWPB4P9evX18g51KE01yia6a6P1BFVMRRfoYj8/HwkJiaiefPm+jZFI3h5ecHFxQUxMTGoW7cuAGFu6KVLl7By5Ur9Gqe3KS5lgI4dO5JatWqRuLg4EhcXR2rWrEm6du0qtY23tzc5fPgwIYSQwsJC0r17d1KxYkVy9+5dkpqaKv7Lz8/XxyWofA2EEPLhwwcSHx9PTp06RQCQffv2kfj4eJKamqoTm/ft20e4XC7Zvn07SUhIIJMnTyaWlpYkOTmZEELIrFmzyJAhQ8Tbv3jxglhYWJApU6aQhIQEsn37dsLlcsnBgwd1Yq88VL0OQgiJj48n8fHxpH79+iQoKIjEx8eTf/75Rx/mi1H1Ovbs2UNMTEzIxo0bpdpAZmamvi6hTPPy5UsSHx9PFi5cSKysrMTP2KdPnwghhHz9+pX4+/uTNm3akDt37pDY2FhSsWJFMmHCBD1brhxXr14la9euJfHx8eTFixdk//79xM3NjXTv3l3fpilNSW2MbUybNo1cvHiRvHjxgly7do107dqVWFtbs+p6Pn36JG4rAMTPmKiSyIoVK4itrS05fPgwefDgARk4cCBxdXUl2dnZerWbikIt8uHDBzJo0CBibW1NrK2tyaBBg8jHjx+ltgFAIiMjCSHfSrjI+rtw4YLO7SdE9WsgRFi6QtY1hIaG6szujRs3Eg8PD2Jqakrq1atHLl26JF4XHBxMAgMDpba/ePEiqVu3LjE1NSWenp5k8+bNOrNVEapeh6z77uHhoVujZaDKdQQGBsq8juDgYN0bTiHBwcEl+qSXL1+SLl26EHNzc+Lg4EAmTJhA8vLy9Ge0Cty+fZs0btyY2NraEjMzM+Lt7U1CQ0NJTk6Ovk1TCUVtjG18//33xNXVlXC5XOLm5kZ69+6t986tqly4cEGhHxMIBCQ0NJS4uLgQHo9HWrRoQR48eKBfowkhHEL+y6inUCgUCoVCoZRZ6OxjCoVCoVAoFAoVhRQKhUKhUCgUKgopFAqFQqFQKKCikEKhUCgUCoUCKgopFAqFQqFQKKCikEKhUCgUCoUCKgopFAqFQqFQKKCikMIAwsLCUKdOHfHnYcOGoWfPnjq3Izk5GRwOB3fv3tXqeTw9PREeHq7Vc1AolLIN9TMUdaCikCKTYcOGgcPhgMPhgMvlonLlypg+fTpycnK0fu6ff/4ZUVFRSm2rKyEHADVr1sTIkSNlrtu7dy+4XC7evn2rdTsoFArz4fP5aNq0Kfr06SO1PCsrC+7u7pg3b57M/aifoegTKgopcunYsSNSU1Px4sULLFmyBJs2bcL06dNlbltYWKix89ra2sLOzk5jx9MUISEhOHDgAL58+VJsXUREBLp27QpnZ2c9WEahUJiGsbExduzYgejoaOzevVu8/Mcff4SDgwMWLFggcz/qZyj6hIpCilx4PB5cXFzg7u6OoKAgDBo0CEePHgXwLeQbERGBypUrg8fjgRCCrKwsjB49Gk5OTrCxsUHr1q1x7949qeOuWLECzs7OsLa2RkhICPLy8qTWFw0fCwQCrFy5ElWrVgWPx0OlSpWwdOlSAICXlxcAoG7duuBwOGjZsqV4v8jISPj6+sLMzAw+Pj7YtGmT1Hlu3LiBunXrwszMDA0aNEB8fLzC+zFkyBDk5+fjjz/+kFqekpKC8+fPIyQkBM+fP0ePHj3g7OwMKysrNGzYELGxsXKPKWukMzMzExwOBxcvXhQvS0hIQOfOnWFlZQVnZ2cMGTIE6enp4vUHDx5EzZo1YW5ujnLlyqFt27Y6GdWlUCjyqVatGpYvX44ff/wRb968wbFjx7Bv3z7s2LEDpqamMvehfoaiT6gopCiNubm51Ijgs2fPcODAARw6dEjsbLp06YK0tDScPn0at2/fRr169dCmTRtkZGQAAA4cOIDQ0FAsXboUt27dgqurazGxVpTZs2dj5cqVmD9/PhISErBnzx5xT/nGjRsAgNjYWKSmpuLw4cMAgN9++w1z587F0qVLkZiYiGXLlmH+/PnYsWMHACAnJwddu3aFt7c3bt++jbCwMLmjoCLKlSuHHj16IDIyUmp5ZGQknJ2d0alTJ3z+/BmdO3dGbGws4uPj0aFDB3Tr1g0pKSlK3uXipKamIjAwEHXq1MGtW7cQHR2Nt2/fon///uL1AwcOxIgRI5CYmIiLFy+id+/eoK81p1D0z48//ojatWtj6NChGD16NBYsWCCVQ10U6mcoeoVQKDIIDg4mPXr0EH++fv06KVeuHOnfvz8hhJDQ0FDC5XLJu3fvxNucO3eO2NjYkLy8PKljValShWzdupUQQkhAQAAZO3as1PrGjRuT2rVryzx3dnY24fF45LfffpNpZ1JSEgFA4uPjpZa7u7uTPXv2SC1bvHgxCQgIIIQQsnXrVuLg4EBycnLE6zdv3izzWJL8+eefhMPhkOfPnxNCCBEIBMTT05PMnj1b7j5+fn5k/fr14s8eHh5k3bp1cu3/+PEjAUAuXLhACCFk/vz5pH379lLHfPXqFQFAHj9+TG7fvk0AkOTkZLk2UCgU/ZGYmEgAkJo1a5LCwsISt6d+hqIv6EghRS4nT56ElZUVzMzMEBAQgBYtWmD9+vXi9R4eHnB0dBR/vn37Nj5//oxy5crByspK/JeUlITnz58DABITExEQECB1nqKfJUlMTER+fj7atGmjtN3v37/Hq1evEBISImXHkiVLpOyoXbs2LCwslLJDRPv27VGxYkVxL/78+fNITk7G8OHDAQhHIGfOnAk/Pz/Y2dnBysoKjx49KlUP/vbt27hw4YLUtfj4+AAAnj9/jtq1a6NNmzaoWbMm+vXrh99++w0fP35U+3wUCkWzREREwMLCAklJSXj9+nWJ21M/Q9EXJvo2gMJcWrVqhc2bN4PL5cLNzQ1cLldqvaWlpdRngUAAV1dXqRwVEepOHDE3N1d5H4FAAEAYQm7cuLHUOmNjYwBQO+RhZGSEYcOGISoqCgsXLkRkZCRatGiBatWqAQBmzJiBM2fOYM2aNahatSrMzc3Rt29fFBQUyD1eUXuKTtoRCATo1q0bVq5cWWx/V1dXGBsbIyYmBlevXsXZs2exfv16zJ07F9evXxfnXFIoFP0QFxeHdevW4c8//8SqVasQEhKC2NhYcDgcuftQP0PRF3SkkCIXS0tLVK1aFR4eHsUEoSzq1auHtLQ0mJiYoGrVqlJ/5cuXBwD4+vri2rVrUvsV/SxJtWrVYG5ujnPnzslcL0rW5vP54mXOzs6oUKECXrx4UcwOkfPy8/PDvXv3kJubq5QdkgwfPhyvX7/G4cOHcfjwYYSEhIjXXblyBcOGDUOvXr1Qs2ZNuLi4IDk5We6xRCOtqamp4mVFy+vUq1cP//zzDzw9PYtdj0iYczgcNGvWDAsXLkR8fDxMTU1x5MgRpa6HQqFoh9zcXAQHB2PMmDFo27Yttm3bhps3b2Lr1q0l7kv9DEUfUFFI0Rht27ZFQEAAevbsiTNnziA5ORlXr17FvHnzcOvWLQDApEmTEBERgYiICDx58gShoaH4559/5B7TzMwMP/30E2bOnImdO3fi+fPnuHbtGrZv3w4AcHJygrm5uTgpOisrC4BwdvTy5cvx888/48mTJ3jw4AEiIyOxdu1aAEBQUBCMjIwQEhKChIQEnD59GmvWrFHqOr28vNC6dWuMHj0aXC4Xffv2Fa+rWrUqDh8+jLt37+LevXsICgoSj1zKwtzcHE2aNMGKFSuQkJCAy5cvF6tf9sMPPyAjIwMDBw7EjRs38OLFC5w9exYjRowAn8/H9evXsWzZMty6dQspKSk4fPgw3r9/D19fX6Wuh0KhaIdZs2aJqycAQKVKlfC///0PM2bMUCjiAOpnKHpCzzmNFIZSdKJJUUJDQ6Umh4jIzs4mP/74I3FzcyNcLpe4u7uTQYMGkZSUFPE2S5cuJeXLlydWVlYkODiYzJw5U+5EE0II4fP5ZMmSJcTDw4NwuVxSqVIlsmzZMvH63377jbi7uxMjIyMSGBgoXr57925Sp04dYmpqSuzt7UmLFi3I4cOHxevj4uJI7dq1iampKalTpw45dOhQiRNNROzZs4cAIKNHj5ZanpSURFq1akXMzc2Ju7s72bBhAwkMDCSTJk0SbyOZAE4IIQkJCaRJkybE3Nyc1KlTh5w9e1YqAZwQQp48eUJ69epF7OzsiLm5OfHx8SGTJ08mAoGAJCQkkA4dOhBHR0fC4/FI9erVpRLOKRSK7rl48SIxNjYmV65cKbauffv2pHXr1kQgECg8BvUzFF3DIYTOJ6dQKBQKhUIp69DwMYVCoVAoFAqFikIKhUKhUCgUChWFFAqFQqFQKBRQUUihUCgUCoVCARWFFAqFQqFQKBRQUUihUCgUCoVCARWFFAqFQqFQKBRQUUihUCgUCoVCARWFFAqFQqFQKBRQUUihUCgUCoVCARWFFAqFQqFQKBRQUUihUCgUCoVCARWFFAqFQqFQKBRQUUihUCgUCoVCARWFFAqFQqFQKBRQUUihUCgUCoVCARWFFAqFQqFQKBSoKQqvXbuGfv36wdXVFaampnB1dUX//v1x8+ZNje4jSXJyMjgcjvjPyMgI5cqVQ+fOnREXFye1LYfDQVhYmMrX9ebNG4SFheHu3bsq71sS8fHxCAwMhK2tLTgcDsLDw+VuK3mdHA4HNjY2aNq0Kfbu3atxu0SI7m9UVFSJ24aFhYHD4WjNFlXt0Tei++Hk5IRPnz4VW+/p6YmuXbvqwTLN0LJlS7Rs2VKp7STbp7W1NapWrYp+/frh4MGDEAgExfbx9PTEsGHDVLLn6tWrCAsLQ2Zmpkr7FT3XxYsXweFwcPDgQZWOo4gvX74gLCwMFy9eLLYuKioKHA4HycnJGjsfQP2xOlB/rD179AkhBG3btkW5cuWQlpZWbP3YsWNhamqK+Ph4mfvfu3cPHA4Hs2bNknuOp0+fgsPhYOLEiUrbpYvvSFOoLArXr1+PZs2a4fXr11i1ahViY2OxevVqvHr1Ck2aNMGvv/6qkX3k8eOPPyIuLg5XrlzB8uXLce/ePbRq1Urul6wKb968wcKFC7XihEaMGIHU1FTs27cPcXFxGDBggMLt+/bti7i4OFy9ehVbtmxBdnY2goKCsGfPHo3bBgCurq6Ii4tDly5dtHL8ssD79++xatUqfZuhVypXrix+bo8ePYpZs2YhNzcX/fr1Q8uWLZGVlSW1/ZEjRzB//nyVznH16lUsXLhQZVGozrlU5cuXL1i4cKFMUdilSxfExcXB1dVVY+ej/lg9qD82TDgcDiIiIvD161eMGjVKat2ZM2ewdetWzJ07F3Xr1pW5f+3atVG/fn3s3LkTfD5f5jaRkZEAgJCQEM0azxSICvz111/EyMiIdO3alRQWFkqtKywsJF27diXGxsbkxo0bpdpHFklJSQQAWb16tdTyc+fOEQBk5MiR4mUASGhoqCqXRggh5ObNmwQAiYyMVHnfkjAxMSHjxo1TalsA5IcffpBalpycTACQFi1aaNw2VQkNDSUqPjoqI/q+tfFdaBrR/ejYsSOxtLQkqampUus9PDxIly5dNHIugUBAvnz5opFjKUtgYCAJDAxUarsaNWrIXBcREUEAkP79+5fantWrVxMAJCkpSant5d2vCxcuEADkjz/+KLVNIt6/f6+2/1EV6o/Vh/pj1WCTPyaEkG3bthEAJCIighBCSEZGBqlQoQKpV69esee+KJs2bSIAyIkTJ4qt+/r1K6lQoQKpX7++Svbo4jvSFCpZ2aVLF2JsbExevXolc31KSgoxNjYmvXr1KtU+spDnhHJycggA0q5dO/EyWU7owYMHpHv37sTOzo7weDxSu3ZtEhUVJV4v+oEo+leSMyvpuJGRkTKPqwhZTogQQhwdHYm3t7fUsqysLDJt2jTi6elJuFwucXNzI5MmTSKfP3+W2u7AgQOkUaNGxMbGhpibmxMvLy8yfPhw8Xp5jf7kyZOkdu3axNTUlHh6epLVq1cXe8AVOYyi9/Dp06dk2LBhpGrVqsTc3Jy4ubmRrl27kvv370vtJ+uY7969I6NGjSIVK1YkpqampHz58qRp06YkJiZG3q0kR44cIQBIbGxssXWixn/v3j1CCCHPnz8n33//PXF1dSWmpqbEycmJtG7dmsTHx8s9PiHfGvytW7cIj8cjY8aMkVovSxR++PCBjBs3jri5uREul0u8vLzInDlzSF5entR2omdh8+bNxMfHh3C5XLJ582bxc3Xu3DkycuRI4uDgQKytrcmQIUPI58+fSWpqKunXrx+xtbUlLi4uZNq0aaSgoEDq2GFhYaRRo0bE3t6eWFtbk7p165Jt27YRgUAgtZ0mRCEhhHTu3JlwOBySnJwsdW+Cg4PFn/l8Plm8eDGpXr06MTMzI7a2tqRmzZokPDxc6l4X/btw4YLUvT506BCpU6cO4fF45KeffpJ5LlGb//3338mUKVOIs7MzMTMzIy1atCB37txR6h4EBwcTDw8PQsi3Z7bon+icou+sqJjdvn07qVWrFuHxeMTe3p707NmTJCQkFDuPpaUlefr0KenUqROxtLQkZmZmhMPhkGfPnsm839QfU38s61oM3R+L6NSpE7G1tSUpKSkkKCiI8Hg88vDhwxL3y8zMJObm5qR3797F1p0+fZoAIBs3biSEELJv3z7Srl074uLiQszMzIiPjw/56aefin3fskShvOe5qJ8ihJDU1FQyevRoUqFCBcLlcomnpycJCwsrJnA3bdpEatWqRSwtLYmVlRXx9vYms2fPLvGaJTFRdkSRz+fjwoULaNCgASpWrChzG3d3d9SvXx+xsbEQCAQghKi8j5GRahHtZ8+eAQAcHR3lbvP48WM0bdoUTk5O+OWXX1CuXDns2rULw4YNw9u3bzFz5kzUq1cPkZGRGD58OObNmycetpdnt7LHFYWMAgIC0LdvX0ybNk2l6xORlZWFjIwMNGnSRLzsy5cvCAwMxOvXrzFnzhzUqlUL//zzDxYsWIAHDx4gNjYWHA4HcXFx+P777/H9998jLCwMZmZmePnyJc6fP6/wnOfOnUOPHj0QEBCAffv2gc/nY9WqVXj79q1a1wAIQ0LlypXDihUr4OjoiIyMDOzYsQONGzdGfHw8vL295e47ZMgQ3LlzB0uXLkX16tWRmZmJO3fu4MOHD3L36dq1K5ycnBAZGYk2bdpIrYuKikK9evVQq1YtAEDnzp3F11ipUiWkp6fj6tWrSocpPTw8MH78eKxfvx5Tp05F9erVZW6Xl5eHVq1a4fnz51i4cCFq1aolDr/dvXsXp06dktr+6NGjuHLlChYsWAAXFxc4OTmJc79GjhyJ3r17Y9++fYiPj8ecOXPw9etXPH78GL1798bo0aMRGxuLlStXws3NDVOnThUfNzk5GWPGjEGlSpUACPPMfvzxR/z7779YsGCBUtesCt27d8fp06dx5coVeHh4yNxm1apVCAsLw7x589CiRQsUFhbi0aNH4u9g5MiRyMjIwPr163H48GFxKNbPz098jDt37iAxMRHz5s2Dl5cXLC0tFdo1Z84c1KtXD9u2bUNWVhbCwsLQsmVLxMfHo3Llykpfn6urK6Kjo9GxY0eEhIRg5MiRABT7puXLl2POnDkYOHAgli9fjg8fPiAsLAwBAQG4efMmqlWrJt62sLAQ3bt3R0hICCZPnoyuXbuCEILdu3fL/L6oP6b+uCQM2R9v27YN/v7+Yl+7YsUK1KhRo8T9bG1t0adPH+zfvx/v37+XepYjIyNhZmaGoKAgAML8ws6dO2Py5MmwtLTEo0ePsHLlSty4caPE71NZ0tLS0KhRIxgZGWHBggWoUqUK4uLisGTJEiQnJ4vD2fv27cP48ePx448/Ys2aNTAyMsKzZ8+QkJCg2gmVVY9paWkEABkwYIDC7b7//nsCgLx//16tfeQh6qmsXLmSFBYWkry8PHL79m3SsGFDAoCcOnVKvC2KKPABAwYQHo9HUlJSpI7ZqVMnYmFhQTIzMwkhqocrlD2uyCZZvU1ZACDjx48nhYWFpKCggDx58oR0796dWFtbk1u3bom3W758OTEyMiI3b96U2v/gwYMEADl9+jQhhJA1a9YQAFL2FEVWT7Bx48bEzc2N5ObmipdlZ2cTBwcHtXumRfn69SspKCgg1apVI1OmTFF4TCsrKzJ58mS5x5LH1KlTibm5udT1JyQkEABk/fr1hBBC0tPTCQDxiJQqiHqB79+/J+np6cTW1pb06dNHvL7oSOGWLVsIAHLgwAGp46xcuZIAIGfPnhUvA0BsbW1JRkaG1LaiEY8ff/xRannPnj0JALJ27Vqp5XXq1CH16tWTew18Pp8UFhaSRYsWkXLlykmNFmpqpPDPP/8Ut2ERRXvFXbt2JXXq1FF4HkXhYw8PD2JsbEweP34sc52skcJ69epJXW9ycjLhcrlSIVBlRgoJURw+LjpS+PHjR2Jubk46d+4stV1KSgrh8XgkKChI6jySz4zIt7q6uhYbrZKE+mPqj4tei6H7Y0mWLVtGAJDatWuTr1+/Kr2fyDdI+tEPHz4QHo9HBg0aJHMfgUBACgsLyaVLl6RGPAkp3UjhmDFjiJWVFXn58qXUdqLn6J9//iGEEDJhwgRiZ2en9DXKQ+MlaYTXCpVm2qiyz08//QQulwszMzPUr18fKSkp2Lp1Kzp37ix3n/Pnz6NNmzZwd3eXWj5s2DB8+fKl2Gw5ZdHWcQFg06ZN4HK5MDU1RfXq1fHnn39i7969qF+/vnibkydPwt/fH3Xq1MHXr1/Ffx06dACHwxEnuzds2BAA0L9/fxw4cAD//vtviefPycnBzZs30bt3b5iZmYmXW1tbo1u3bmpf19evX7Fs2TL4+fnB1NQUJiYmMDU1xdOnT5GYmKhw30aNGiEqKgpLlizBtWvXUFhYqNQ5R4wYgdzcXOzfv1+8LDIyEjweT9zjc3BwQJUqVbB69WqsXbsW8fHxMmfLlkS5cuXw008/4dChQ7h+/brMbc6fPw9LS0v07dtXarloZuy5c+eklrdu3Rr29vYyj1V0VrOvry8AFEtQ9/X1xcuXL4vZ0bZtW9ja2sLY2BhcLhcLFizAhw8f8O7dO8UXqgaidq6IRo0a4d69exg/fjzOnDmD7Oxslc9Tq1YtuaO0sggKCpLyPR4eHmjatCkuXLig8rlVIS4uDrm5ucVmX7u7u6N169bFngMOh1Os7dnZ2RX7XiWh/pj6Y0UYsj/OycnBtm3bYGRkhKdPn6o06z8wMBBVqlQRj8IBwO7du5Gfn48RI0aIl7148QJBQUFwcXER+9DAwEAAKPH+KcvJkyfRqlUruLm5ST1XnTp1AgBcunQJgPD7yMzMxMCBA3Hs2DGkp6erdT6lRWH58uVhYWGBpKQkhdslJyfD3Nwc5cqVU2ufkpg0aRJu3ryJ27dv4/nz50hNTcXo0aMV7vPhwweZM/7c3NzE69VBW8cFIC4PcfXqVWzduhXW1tYYMGAAnj59Kt7m7du3uH//PrhcrtSftbU1CCHih6JFixY4evQovn79iqFDh6JixYrw9/dXWFLh48ePEAgEcHFxKbZO1jJlmTp1KubPn4+ePXvixIkTuH79Om7evInatWsjNzdX4b779+9HcHAwtm3bhoCAADg4OGDo0KEySw9IUqNGDTRs2FDcwPl8Pnbt2oUePXrAwcEBgPAH8Ny5c+jQoQNWrVqFevXqwdHRERMnTpRZZkYRkydPhpubG2bOnClz/YcPH+Di4lLsR9fJyQkmJibFnhtFs1VF9oswNTWVuzwvL0/8+caNG2jfvj0A4LfffsPff/+NmzdvYu7cuQBQ4nehDiLxImofspg9ezbWrFmDa9euoVOnTihXrhzatGmDW7duKX0eVWf3ynvGS9N+lUF0fHk+pOj5LSwsxIJA5Fuzs7OlvteiUH9M/bEiDNkfz5gxAykpKTh16hQsLS0xYsQIpTqmovOPGDECDx48EPueyMhIeHl5oVWrVgCAz58/o3nz5rh+/TqWLFmCixcv4ubNmzh8+DAAzfnQt2/f4sSJE8WeK1EoXPRcDRkyBBEREXj58iX69OkDJycnNG7cGDExMSqdT+mcQmNjY7Ru3Rp//vknXr9+LTO34/Xr17h9+zY6duyo9j4lUbFiRTRo0EBZswEIR29SU1OLLX/z5g0AoYNVB20dFxDm5IiuMyAgAL6+vggMDMSUKVNw8uRJ8fHNzc0REREh8xiS5+/Rowd69OiB/Px8XLt2DcuXL0dQUBA8PT0REBBQbF97e3twOByZDbzoMtEPVX5+vtRyWU54165dGDp0KJYtWya1PD09HXZ2djKvQ/J6wsPDER4ejpSUFBw/fhyzZs3Cu3fvEB0drXDf4cOHY/z48UhMTMSLFy+QmpqK4cOHS23j4eGB7du3AwCePHmCAwcOICwsDAUFBdiyZYvC40tibm6OsLAwjB49ulh+ICB8bq5fvw5CiJQwfPfuHb5+/VrsudFGfat9+/aBy+Xi5MmTUiMPR48e1fi5RBw/fhwcDgctWrSQu42JiQmmTp2KqVOnIjMzE7GxsZgzZw46dOiAV69ewcLCosTzqHq/5D3jkqLIzMysWDkdAGr3xgGIjy/PhyjyHyLfKuv5EkH9sWaOC1B/LO96mOqPz507hy1btmD+/Pno2LEjNm7ciP79+2P9+vVK1xccNmwYFixYgIiICHC5XMTHx2Px4sVi/3L+/Hm8efMGFy9eFI8OAlA655HH4xX7joDi31P58uVRq1YtLF26VOZxJDvZw4cPx/Dhw5GTk4PLly8jNDQUXbt2xZMnT+TmcRdFpfDxrFmzQAjB+PHji9Xw4fP5GDduHPh8PiZNmlSqfTRNmzZtxF+gJDt37oSFhYU4WZjH4wFQXuEre1xN0Lx5cwwdOhSnTp0Sh0G6du2K58+fo1y5cmjQoEGxP09Pz2LH4fF4CAwMxMqVKwFAbj0xS0tLNGrUCIcPH5Yaifj06RNOnDghta2zszPMzMxw//59qeXHjh0rdlwOhyO+zyJOnTqlVAhFkkqVKmHChAlo164d7ty5U+L2AwcOhJmZGaKiohAVFYUKFSqIR8pkUb16dcybNw81a9ZU6vhFGTFiBHx9fTFr1qxiYY82bdrg8+fPxQTYzp07xeu1DYfDgYmJCYyNjcXLcnNz8fvvv2vlfJGRkfjzzz8xcOBA8cSWkrCzs0Pfvn3xww8/ICMjQxz+UbWdlsTevXulRhBevnyJq1evShXs9vT0xJMnT6Sc+IcPH3D16lWpY6liW0BAAMzNzbFr1y6p5a9fvxaHQhUhWWCX+mPqj0WUdX+cnZ2NESNGoHbt2pg3bx4AoF+/fujbty9mz56N58+fK3VNbm5u6NixI/bu3YuNGzfCyMgIwcHB4vUicVj0/m3dulWp43t6ehb7js6fP4/Pnz9LLevatSsePnyIKlWqyHyuZEVeLC0t0alTJ8ydOxcFBQX4559/lLIJUGGkEACaNWuG8PBwTJo0Cd999x0mTJiASpUqISUlBRs3bkRcXBzCwsLQrl27Uu2jaUJDQ8Vx+QULFsDBwQG7d+/GqVOnsGrVKtja2gIAqlSpAnNzc+zevRu+vr6wsrKCm5ub3HCXssfVFIsXL8b+/fsxf/58xMbGYvLkyTh06BBatGiBKVOmoFatWhAIBEhJScHZs2cxbdo0NG7cGAsWLMDr16/Rpk0bVKxYEZmZmfj555+l8h/kna9jx45o164dpk2bBj6fj5UrV8LS0hIZGRni7TgcDgYPHoyIiAhUqVIFtWvXxo0bN2QWdu3atSuioqLg4+ODWrVq4fbt21i9erXCWYWAcLZfq1atEBQUBB8fH1hbW+PmzZuIjo5G7969S7x3dnZ26NWrF6KiopCZmYnp06dLzay8f/8+JkyYgH79+qFatWowNTXF+fPncf/+fYXV7eVhbGyMZcuWoVevXgAgnlEHAEOHDsXGjRsRHByM5ORk1KxZE3/99ReWLVuGzp07o23btiqfT1W6dOmCtWvXIigoCKNHj8aHDx+wZs2aYg5OVXJzc3Ht2jXx/1+8eIGjR4/i5MmTCAwMLLGH361bN/j7+6NBgwZwdHTEy5cvER4eDg8PD/FM3Jo1awIAfv75ZwQHB4PL5cLb2xvW1tZq2fzu3Tv06tULo0aNQlZWFkJDQ2FmZobZs2eLtxkyZAi2bt2KwYMHY9SoUfjw4QNWrVoFGxsbqWNZW1vDw8MDx44dQ5s2beDg4IDy5cvLFAR2dnaYP38+5syZg6FDh2LgwIH48OEDFi5cCDMzM4SGhiq0u1mzZujQoQOio6OpP1bhuJqC+mNm+uMpU6YgLS1NHHIVsWnTJtSoUQMjRowQv82oJEJCQnDq1Cls27YNHTp0kMpXbdq0Kezt7TF27FiEhoaCy+Vi9+7duHfvXonHBYQ+Zf78+ViwYAECAwORkJCADRs2FHtOFy1ahJiYGDRt2hQTJ06Et7c38vLykJycjNOnT2PLli2oWLEiRo0aBXNzczRr1gyurq5IS0vD8uXLYWtrK85jVQp1ZqdcvXqV9OnThzg7OxMjIyMCgJiZmUnNONPEPpLIq4slC8ipi9WtWzdia2tLTE1NSe3atWXOztq7d6+4Hpys4xRF2eNCxdlu8radMWMGAUAuXbpECCHk8+fPZN68ecTb25uYmpqK67pNmTKFpKWlEUKEta06depEKlSoIK731LlzZ3LlyhXxceXNWDt+/DipVasWMTU1JZUqVSIrVqyQOZMqKyuLjBw5kjg7OxNLS0vSrVs3cYFXyXv48eNHEhISQpycnIiFhQX57rvvyJUrV4rN7ixqT15eHhk7diypVauWuLaXt7c3CQ0NJTk5OUrd17Nnz4rrkj158kRq3du3b8mwYcOIj4+PuMZTrVq1yLp160qctSY5+7goTZs2JQBk1ikcO3YscXV1JSYmJsTDw4PMnj1bbp3Coohmshad6SjPFlGdO0kiIiKIt7c34fF4pHLlymT58uVk+/btxWb2qjL7WHR/ARBLS0tSuXJl0rdvX/LHH38QPp9fbJ+iM+3+97//kaZNm5Ly5cuLn7mQkBCp2oaEEDJ79mzi5uYm9iVF6xTKQlGdwokTJxJHR0fC4/FI8+bNpWaVitixYwfx9fUlZmZmxM/Pj+zfv7/Y7GNCCImNjSV169YlPB6PQIk6hdu2bRO3MVtbW9KjRw/xjEIRsr4/Qr5939Qfq3Zc6o+FGJo/FtURXLp0qcz1Bw4cIADIzz//rJSNBQUFxNnZWWa1CEKE7SggIIBYWFgQR0dHMnLkSHLnzp1i352s7yg/P5/MnDmTuLu7E3NzcxIYGEju3r0rs07h+/fvycSJE4mXlxfhcrnEwcGB1K9fn8ydO1dcE3HHjh2kVatWxNnZmZiamhI3NzfSv3//YjUnS0IjJbZ37NhBAJCZM2dqdR8KhUKhKIb6YwqFoi4qhY/lMXToUKSmpmLWrFmwtLRUqvCtOvtQKBQKRTHUH1MoFHXhEKLkHG0KhUKhUCgUisGi8eLVFAqFQqFQKBT2QUUhhUKhUCgUCoWKQgqFQqFQKBQKFYUUCoVCoVAoFFBRSKFQKBQKhUKBim80KcsIBAK8efMG1tbWWnkXLYVCUR9CCD59+gQ3NzepNyNQFEP9GoXCXPTh16goVJI3b95IveKGQqEwj1evXpX4ii7KN6hfo1CYjy79GhWFSiJ6r+qrV6+Kve+UQqHol+zsbLi7u6v9/uOyCvVrFApz0Ydfo6JQSUShFRsbG+o8KRSGQkOgqkH9GoXCfHTp12jyDYVCoVAoFAqFikIKhUKhUCgUChWFFAqFbeTmAhERAH1tO4VCMRD4fAGert2CU1cSEff8A/gC/fg3mlNIoVDYQ2wsMHYs8Pw5YGEBDBigb4soFAqlVFw++RcsJv2IBi/u4u96XfFDu7FwtTXD9Fa6rwxARSGFQmE+794B06YBu3YJP1eoANCZxhQKhYXwBQQ3kjLw7n0meOv+h1aHtoHHL0SuCQ//2jgBANKy8jB1/z2d20ZFIYVCYS6EAJGRwIwZQEYGwOEAP/4ILF4M0NmyFAqFZUQ/TMXCEwlwf3gLy6I3oGrGawDAJa96mNd+PF7ZuQAA9JUcQ0UhhUJhJomJwlDx5cvCz3XqAL/+CjRsqFezKBQKRR2iH6Zi1m+XMOtiJAbcPwsAeG9hh0VtRuGEbwthp1cCfQhDKgopFAqzyMsDli8X/hUWCnMHFy0CJk0CTKjLolAo7IPPF+Daol8Qe2ozyn/JAgDsqd0BK1oOR7aZlZ6t+wb1sBQKhTlcuCAcHXzyRPi5c2dg40bA01OvZlEoFIq68J88xfO+QxD24DoA4Em5SpjdcQJuV/TTs2XFoSVpKBSK/klPB4YNA1q3FgpCFxfgwAHg5EkqCBVw+fJldOvWDW5ubuBwODh69Ki+TaJQKCIKCvBk4ix8rVED1R9cR56JKVa1GIouw39WShDq4/1MVBRSKBT9QQiwYwfg4yP8l8MBxo8HHj0C+vUrlmNDkSYnJwe1a9fGhg0b9G0KhUKR5K+/8MmvJqqvXwne10Jc9qyLDiM2YFNAfxQac/VtnVxo+JhCoeiHJ0+EoeILF4Sfa9YEtm4FAgL0a1cp4fP5ePDgATw8PGBvb6/Vc3Xq1AmdOnXS6jkoFIry8D9kIH3CFDjv2wlrAOkWtljceiSO+bVUqZMrrFNYDX3DtWWpbOhIIYVC0S35+cKJIzVrCgWhmRmwYgVw+zYrBeHkyZOxfft2AEJBGBgYiHr16sHd3R0XL17Ur3FFyM/PR3Z2ttQfhUIpPXy+AH/OWYdMjypw3rcTALCvVnu0GbkFx2q0UkkQTmlbDX/91Brt/Fy0Za5c6EghhULRHZcvA2PGCMPDANChA7BpE1C5sn7tKgUHDx7E4MGDAQAnTpxAUlISHj16hJ07d2Lu3Ln4+++/9WzhN5YvX46FCxfq2wwKxWDgCwh27j6Pqgt/QqfntwEAzxwqYk7HCbjh7q/SsVxtzRDazQ8d/V21YapS6FQU3rlzB1wuFzVr1gQAHDt2DJGRkfDz80NYWBhMTU11aQ6FQtEVGRnAzJnAfyNqcHYGwsOB779nfd5geno6XFyEPfrTp0+jX79+qF69OkJCQvDLL7/o2TppZs+ejalTp4o/Z2dnw91d96/SolDYjOiNJOfuv4LFxvUYd2k3zL/mI9+Yi40B/bGlcV8UmCifN2hrboJNg+qjSeVyMDbSrz/Uafh4zJgxePJfqYkXL15gwIABsLCwwB9//IGZM2fq0hQKhaILCBG+ms7H55sgHD1aWJh6wADWC0IAcHZ2RkJCAvh8PqKjo9G2bVsAwJcvX2BsbKxn66Th8XiwsbGR+qNQKMrBFxD8HPsU9RfHYFVYFPqM6YWp5yJg/jUfVyvVQscRG/BLs4EqCUIOgJV9aqFZ1fJ6F4SAjkcKnzx5gjp16gAA/vjjD7Ro0QJ79uzB33//jQEDBiA8PFyX5lAoFG3y7BkwbhwQGyv87OcnfCNJs2b6tUvDDB8+HP3794erqys4HA7atWsHALh+/Tp8fHz0bB2FQiktfAHBhvPPsPXyc5hkZ2HG5Z0YFP8njECQYW6DJa1DcLhGa5U7ufYWXCzvXVOv4eKi6FQUEkIgEAgAALGxsejatSsAwN3dHenp6bo0hUKhaIuCAmD1auH7ifPzAR4PWLAAmD4dMMAUkbCwMPj7++PVq1fo168feDweAMDY2BizZs3S6rk/f/6MZ8+eiT8nJSXh7t27cHBwQKVKlbR6bgqlLBD9MBWzDj9AZk4Bujz6C6HnfoVTzkcAwB/+bbGs1XB8tLBV6ZhWPGOMal4ZE1pXY8TooCQ6FYUNGjTAkiVL0LZtW1y6dAmbN28GIHRkzs7OujSFQqFog7/+Ek4kSUgQfm7bFti8GahaVb92aZm+ffsWWxYcHKz18966dQutWrUSfxblCwYHByMqKkrr56dQDJnoh6kYu+sOKma9xdqzm9H6xS0AwAt7N8ztMAFxHrVUPqaDJRfXZreFqQkzi7/oVBSGh4dj0KBBOHr0KObOnYuq//1QHDx4EE2bNtWlKRQKRZN8/AjMmiUMDwOAoyOwbh0QFGQQeYNFUWUCycSJE7VmR8uWLUEI0drxKZSyhmgSyZuPX7D4+AOMun4YU/7eDYvCfBQYmWBzk37YFNAP+SaqRz04AJb1qslYQQgAHMIAj5KXlwdjY2Nwucyt8p2dnQ1bW1tkZWXR5GwKRQQhwL59wOTJwLt3wmUhIcCqVYCDg8ZPJ3LY7z7lwcnaDI28HGBsxNF5+/Ty8lJqOw6HgxcvXmjZGvWhfo1S1hH5lLSsXPz9LB0xie+QlVuI2m8eY/mZDfB7lwQAuO7ujzkdfsDzcurN1len3Iw+2qfO6xRmZmbi4MGDeP78OWbMmAEHBwckJCTA2dkZFSpU0LU5FApFXV68EL6S7swZ4WcfH+EbSVq0ACBfwIkoaX1Roh+mYuGJBKRm5YmXiRxt00qW2rlGOSQlJen0fBQKRXOIfE9MQhqO3n2DjJwC8Tqr/C8IvfI7gm+fhBEIPppZY1mr4fijZjuVoh4WXCN0rumKZtUc4WJTsn9jCjoVhffv30ebNm1gZ2eH5ORkjBo1Cg4ODjhy5AhevnyJnTt36tIcCoWiDoWFwNq1wMKFQG6ucPLIvHnCOoT/TbJQJOA6+ruWuL4o0Q9TMW7XHRQNa6Rl5WHcrjtY07OaVi6VQqGwF8lRwIycAthZmCLu+bfRQCkIQYcncVgYuwUunzMAAIdqtMLS1iORocJEEjtzLoY382TkJBJl0KkonDp1KoYPH45Vq1bB2tpavLxTp04ICgrSpSkUCkUdrl0T1hl88ED4uVUr8Ddtxg1uebxLTIeTtRk+5hTghz3yBdzoFl749XKS3PWbB9eTEoZ8AcHCEwnFtgcAAmGezoo/H2nuGtXg9evXOH78OFJSUlBQUCC1bu3atXqyikIpeygaBZSHW/Y7LIzZinbPrgMAku1cMbfDD/jbs45S57TiGeP7Bu5o6+fCmhFBeehUFN68eRNbt24ttrxChQpIS0vTpSkUCkUVsrKA2bNBtmwBhxDk29kjZe4SPG3XE4uPJCI161tZFCMO5Ao4APjtSnFBKFrPAbDwRALa+bmIHeuNpAypEUVZ+73NzlfzwkrPuXPn0L17d3h5eeHx48fw9/dHcnIyCCGoV6+e3uyiUMoasiIQijAW8DHs9glMvbILloV5KDAywdbGfbAhoD/yubwS97c0NcboFswsLaMuOhWFZmZmMl/A/vjxYzg6Omr13JcvX8bq1atx+/ZtpKam4siRI+jZs6dWz0mhsB5CgIMHgYkTgbQ0cCBRmyvdFtgbX2wXQQlT1xStJwBSs/JwIykDAVXKAQDefVLOweuL2bNnY9q0aVi0aBGsra1x6NAhODk5YdCgQejYsaO+zaNQygSn76di/J47Sm/vn/YMy6PXo+bb5wCAmxX8MKfDD3jq6FHivkyuM1hadCoKe/TogUWLFuHAgQMAhDPzUlJSMGvWLPTp00er587JyUHt2rUxfPhwrZ+LQjEE+C+SkD1yDOwvxAAAkuzdMEfN2lyqIikEnazNtH6+0pCYmIi9e/cCAExMTJCbmwsrKyssWrQIPXr0wLhx4/RsIYVi2Jy+/wYTZHRQZWGZ/wXTruxC8J2TMCYCZPEssazVCByo1Q6EU3KpGKbXGSwtOhWFa9asQefOneHk5ITc3FwEBgYiLS0NAQEBWLp0qVbP3alTJ3Tq1Emr56BQ2EbRGcD1Pexx+/l7fF65Gt/t2gB7DdTmUgdJIdjIywGutmZIy8qTGXbmAHC24eGVTiwrjqWlJfLzheFrNzc3PH/+HDVq1AAA+qYmCkXLCEcIlROE7Z5ew8KYLXD7JGyXR/0CsaT1SKRb2iu1PxvqDJYWnYpCGxsb/PXXXzh//jzu3LkDgUCAevXqiV8gT6FQtIOk+CtvyQM4wLnEt8USseukPcHSPzcg4J2wtl5pa3PJwogjjErLE3gutsLyDSKMjTgI7eaHcbvugAPp/USBm1mdfNB3kcZMVIkmTZrg77//hp+fH7p06YJp06bhwYMHOHz4MJo0aaIfoygUA4cvIPjl3FP8cu5pidu6ZKdjYewWdHh6DQCQYuuMee3H43Ll+kqfT506g2xE53UKAaB169Zo3bq1Pk6tNPn5+eLePwCZuZAUCtMRvcg98u8kZBYtwSCBVf4XTJOozZVpZoWlrUbgYM22SoVUlEEk4EY1F84+lifwQrv5FcvT6ejvis2D6xVLInfRU51CSdauXYv/t3ff8TXdbwDHPzd7ESKIEUkIJbaoUdRO0J9a1VKUUmoEQYdRQkmoaqlN1apWtTVqxqramwhiCyESREQIWfee3x+3uRXZkdyb8bxfL69XzrjnPLk39+s553y/z/fZs2eAdh7kZ8+esW7dOlxdXZk9e7bB4hKioNLNR/w87TYNwEijps/Z7Xx2YDVF4l+QYGTMjw26MPetHsSapt8txdbChLZupfNdncHXletJYV6ZDiqrpk+fzpQpUwwdhhBZ9nJJht9P3eVZXGLaO6dSm2tD9Zb4thzAI+tirxWHkSr5oBKHl66061YonmaCl9aVeLsaZWjr5pDmjCaGUrFiRd3PVlZWLFy40GCxCFGQJV3kzt5zNcN9q9+/gZ//fGqHa+8kni5blfHtvLhS0jnFvjbmxnR3L0/54lbY2ZgXqiTwVbk+zV1enA5KpVJlOPo4tTuFjo6OMh2UyNOyUpKhTPRDvt69ONu1udKS1Iwu+LAuxa3Nc2xGk/TIdG3ZI++byIvSKjq9K+g+0bHpXOQCVvEv8D70KwNO/YWxoiHa3Jpvmvfl1zrtUjz1yOuFpgvkNHf5dTooc3NzzM0zrlMkhKElNaC7Loax4sjtDPc31qjpe3orYw7+jHVCLAlGxixp2I15jT/IVG2ujGR0x08Xh5FKV3YmPzMyMkKVzvRXarVaj9EIkb9ltdbgy1pdP8HXuxdRPvohAFurNuPr1gNp37YuX9lZUczKjKjn8YX+bmB6DNKn0BCePXvG9ev/FdgNDg4mICAAOzs7KlSoYMDIhMicLE3ZlIbXqc2VmjK2Fkx8p1q6dwQLuo0bNyZbTkhI4OzZs6xatUq6oAiRBWlNZ5mRUk8f4bN3Ke9cOQzA3aKl+MpjCP9UepOFH9alQ62yOR9sAZXrSeHo0aOZOnUq1tbWjB49Ot19c3M6qFOnTtGyZctkcQH07duXlStX5tp5hXhdmR0skh7ruOeMPvQL/U5v0dXmmtHiY36r7ZHpgSRJA0NGtamMs711oUwAU9OpU6cU69577z2qV6/OunXrGDBggAGiEiJ/iU/UMH7jhSwlhEYaNb0CdvDF/lUUiX9BosqIZQ268MNbPYkzt2Bhz3p0qFWwRwvntFxPCs+ePUtCQoLuZ0Np0aIFudx9UojXptYoHLvxiKM3I9AocD86lh0Xwnken/1HkK9bmytJZh8LC62GDRsycOBAQ4chRJ6WdNG79MANYrLQzlV9EMx0//nUDbsCwNkybzC+3TAuldIO/FrYs64khNmQ60nhvn37Uv1ZCPGfpIZxyYEbr5UAviw7tbleHTFsZ21KlzrlCsRE7/r04sUL5s2bR/ny5Q0dihB5VmZLy7zMIiEW78Nr+eTERkwUDdFmVsz8dyCJxsiY4lamTO9aUy5es0mvfQr79+/PDz/8QJEiRZKtj4mJYfjw4Sxfvlyf4QiRJ2SnYUxPVmtzvZz4uTsV5/Ttx4W2f2B2FC9ePNlAE0VRePr0KVZWVqxZs8aAkQmRd2V1rmKA5jdPM23XQhyf3Nceo8pbTGkziPtF7PP8SOL8ItdL0rzM2NiYsLAwSpUqlWx9REQEDg4OJCamP9TckKR0g8gN2WkY0+N2/yZ+O+dRJyz12lzFLE3p+5YTDVxKEPEsrsAkfob8fq5cuTJZUmhkZETJkiVp2LAhxYtn7RG9vkm7Jgwhaa5iTSazj5LPHjNp71I6Xj4IwN2iJfFpO5i9rg0BbT/ngpgMFsiSNKD9xRRF0V1BW1j8d7dCrVazffv2FImiEAXd1oB7DF+XM/1sLeNjGXXoF/qf+kv7SMXcmpnN+/JLnXagMuLjt5zxqC6PgHNDv379DB2CEPlGVuYqVikaep7bydh/VlI0Lga1yojl9d9ldtNePDezlEfFuUAvSWGxYsVQqVSoVCqqVKmSYrtKpZLSDaLQUGsURv52lq2BYTlyvJY3TjJ11yLKRz8AYOsbTZnSZhAPbbTzB0tJhpwXGBiY6X1r1aqVi5EIkfclldPaeTGMVUczrqUKUOXhLfx2LqB+6CUAAh1cGefpxUUHV4pZmvKpPCrOFXpJCvft24eiKLRq1Yr169djZ/ffZPdmZmY4OTlRtqz8pyUKppdHFF978Ix/rjwgLvH1e22kV5sLCs8E7oZQp04dVCqVrqKBFK8WIqXslNMyT4hjxJHfGHRiA6YaNTFmllzz+oIzHXvxia2VFJ3OZXpJCps3bw5oC0Y7OjpiZJS5umhC5Hc5PYgEtI9Uep3V1uYqGv+cRJURP73ZmRWtP6JpHSdmF7IJ3A3h5Zmazp49y2effcbnn39O48aNATh69CjfffcdM2fONFSIQhhMdqspNAs+w7RdC3GKCgdgV+VGmC2cR4s29amTS7GK5PQ6+tjJyYmoqChOnDjBgwcP0Gg0ybZ/9NFH+gxHiFzlfyGMwWtybhAJaGtzfbNrPrVDtbW5HlSrzYVJM6n1pjuHJQnUGyen/2aA6d69O3PnzqVDhw66dbVq1cLR0ZGJEyemO8e6EAVNdi6ES8REMfHvH+kctB+AMJsSzPyfF54TPqWFPOnQK70mhVu2bKFXr17ExMRQpEiRZI9cVCqVJIWiwIhP1DDm93M5djyLhFi+PL6Ovkc3YKRRQ5Ei4OdHqSFDaGVsnGPnEVl3/vx5XFxcUqx3cXEhKCjIABEJYRhZraagUjS8H7ibcf+soFjsM9QqI1bXe4fnEyczq2Nducg1AL0mhWPGjKF///74+flhZWWlz1MLoTf+F8IY88e5LFXnT42nW2nqO9vhFngE95lfYXHn3w7aXbvC3LlQrlwORCteV7Vq1Zg2bRo//fSTrrJCXFwc06ZNo1q1agaOTgj9SCozk1mVIu7gt3M+De9eBOBC6UqM8/RiyJj3ZWCcAek1KQwNDWXEiBGSEIoCK6ceGc/vUZf/ORiBtzesW6dd6egICxZAx46vfXyRcxYvXkzHjh1xdHSkdu3aAJw7dw6VSsXWrVsNHJ0QuSup/+DsPVcztb95YjxDj/7OkGN/YqZJ5LmpOd817c3qN9/lh15vytR0BqbXpNDT05NTp05RsWJFfZ5WCL1QaxTGbjj/2sf5tKkT/zuxFb78EqKiwOjf5HDKFLCxee3ji5zVoEEDgoODWbNmDZcvX0ZRFD744AM+/PBDrK2tDR2eELnG/0IYkzdfJDw6LlP7v3UrgGm7FlLx8T0A9lR6E5+2Qwi1LfVv6SxJCA1Nr0nhO++8w+eff05QUBA1a9bE1NQ02fZ3331Xn+EIkSOSSs74bL7wWqOMbcyNWVjLjLenfwpHjmhXurvD0qVQr14ORStyg5WVFYMGDTJ0GELoTVb6D9o9f8KEfT/R7cLfANy3sWNy60HseKMJZYpZslhKZ+UZek0KBw4cCMDXX3+dYptKpZJ6XiLf2R4YxhfrA3kW93pTNHatWoxZV7dh1ONbSEzU3hGcOhWGDwcZSJLnbN68mfbt22NqasrmzZvT3VcudkVBotYozN17jbl7r2W8s6LQ/fwexu9bTvHYp2hQ8XO9Dixq8zHvNK3KWjeZZSmv0WtS+GoJGiHys+nbg1hyIDjjHdNhZ23K4lKRNJg2Em7c0K7s1AnmzdP2IRR5UufOnQkPD6dUqVLplpyRi11RkGSl3EzFR3fx2zmfRncuAHCppDNTOo6kcc8OHJaZSPIsvSaFQhQUWwPuvVZC+PFbTnRwMMF9zlSMJv2qXVmunDYZ7NIlh6IUueXlC1y52BWFQWYfF5slJjD02O8MOfYH5upEXpiY80PTnlh98Rm/eLpJMpjH6T0pjImJYf/+/YSEhBAfH59s24gRI/QdjhBZtjXgHl6/Zb70wstszE2Y1a0G7U76Q7/P4fFjUKm0j4mnToWiRXM4WmEIUVFRFCtWzNBhCJEjMltuplFIIL47F1Ip8i4A/7i485XHEMYPbS9lZvIJvSaFZ8+epUOHDjx//pyYmBjs7OyIiIjAysqKUqVKSVIo8rzXeWRsYWrEmffKY+b1IRw4oF1Zty4sWQJvvpmDUQp9+uabb3B2duaDDz4AtDOcrF+/njJlyrB9+3ZdmRoh8pvMlpsp9iKa8fuW8/75PQA8tC7GlNaDON2wLT7vVpdBJPmIXichHjVqFB07diQyMhJLS0uOHTvG7du3cXd3Z9asWfoMRYgs2x6Y/UfG5onxbHmwCzP3utqE0MoKvvsOTpyQhDCfW7JkCY7/9v/cvXs3e/bswd/fn/bt2/P5558bODohsk6tUfhhzzXqfb0r/YRQUeh6YS97fxysSwh/qdOO1p8spvLwARwa21oSwnxGr3cKAwICWLJkCcbGxhgbGxMXF0fFihWZOXMmffv2pWvXrvoMR4hMU2sUPl8fmK3XNr59jgUHlmB3L0S74p13tEWoX5o/V+RfYWFhuqRw69atvP/++3h4eODs7EzDhg0NHJ0QmZd0Z3DJgRs8z2BGJufIUKbtWkjT29rpPC/bOzG+nRcB5asxv2c9qTmYT+k1KTQ1NdXNd1y6dGlCQkKoVq0atra2hISE6DMUITJNrVHotewYMXFZG0Vq9/wJPvuX0ylwr3ZFmTLa6em6ddP2IxQFQvHixblz5w6Ojo74+/szbdo0ABRFkZHHIt/I7MhiU3UCnx5fz/Aj6zBXJxBrYsYPTXry45tdSDQ2YWFPKUKdn+k1Kaxbty6nTp2iSpUqtGzZkkmTJhEREcHPP/9MzZo19RmKEJmyPTCMz//M4jzGikKPoL34HFiJZXSUNgEcMgT8/MDWNtdiFYbRtWtXPvzwQypXrsyjR49o3749oH0y4urqauDohMhYZqfnrH/3ItP951P50R0ADjjXZYLnMO4Uc6C4lSnTu9aUx8X5nF6TQj8/P54+fQrA1KlT6du3L0OGDMHV1ZUVK1boMxQhMuS7LYgfD2atD2HFR3dZdWI5joEntCtq1dLOSCKPEQus2bNn4+zszJ07d5g5cyY2/05FGBYWxtChQw0cnRDpU2sUpmwJSneforHPGPvPCj48txOAh1bFmNr6EzZXa45KpcK7dWWGt5bagwWBSlEUxdBB5AfR0dHY2try5MkTikrZkAJv6taL/HToVqb3N0tMYMixPxhx4k+ME+LB0hImT4ZRo+CV6RxFzpPvZ/bI+yaO3nhEzx+Ppb5RUXj30gEm7v2Rks+jAFhby4MZLT7miWURgH/nLJZyM7nBEN9PKV4txCt8t2UtIWwYch6/nQt0tblo1w4WLgQXl9wJUOQ5P//8M0uWLOHmzZscPXoUJycn5syZg4uLC506dTJ0eELoqDUKJ4IjCX/ygsiYeA5ce5jqfhUehzFt10LevqWtT3i1RAXGtxvGqfLVAShja4GPzFlc4Og1KXRxcdENNEnNzZs39RiNECltDbjHjwdvZWrfV2tzKaVLo/rhB3j/fRlIUogsWrSISZMm4e3tja+vr25wSbFixZgzZ44khSLP8L8QxpQtQYQ9iU1zH1N1AgNPbGTEkd+wSIwnztiUeW99wJKG3Ugw1j71GNWmMl4yVV2BpNek0NvbO9lyQkICZ8+exd/fX+p5CYPL9EwlikKXi/v46u9llHgRDcDt7h/htPQHkFksCp158+bx448/0rlzZ2bMmKFbX79+fT777DMDRibEf/wvhDFkzRnS6y9W7+4l/HbOp2rEbQAOOdXmK4+h3LIrByCDSQoBvSaFI0eOTHX9ggULOHXqlD5DESKZzA4qebU21xX7Chz/0o+PPuuV2yGKPCo4OJi6deumWG9ubk5MTIwBIhIiObVGYfLmoDQTwqKxz/hi/yp6B+wA4JFlUaa1+oSN1VuCSoW1mTGD3q4odwcLgTzRp7B9+/aMGzdORiALg8jMoBJTdQKDjm9gxJHfdLW5Fr3di6ozffjIXYpQF2YuLi4EBATg9Eox8h07duDm5magqIT4z/y/rxEencojY0Xhf5cP4rN3KSVjogBYV7Mt01t+TJSldmBD+xqlmf+huySDhUSeSAr//PNP7OzsDB2GKIQyM6gktdpce4f7MMn7XWkoBZ9//jnDhg0jNjYWRVE4ceIEa9euZfr06SxbtszQ4YlCbntgGLP3XEuxvnxUOFN3L6LlzdMA3LArz3jPYRyvkLxm8EeNXaSdK0T0Xrz65YEmiqIQHh7Ow4cPWbhwoT5DEYWcWqMwd++1dAeVvFqbK8LKlq9bD6TkwL5M6VhDT5GKvO7jjz8mMTGRL774gufPn/Phhx9Srlw5fvjhB3r06GHo8EQhlDTCeOfFMFYdvZ1sm4k6kQGnNuF9aC2WiXHEGZuwoPEHLG74HvEm/5XPUgEOthY0cJEbNoWJXpPCzp07J1s2MjKiZMmStGjRgqpVq+ozFFGIbQ8MY8Km8zxOazqndGpzve9RkwnvVNdfsCJfGDhwIAMHDiQiIgKNRkOpUqUACA0NpVy5cgaOThQWSXMXrzgcTNSLlO1bnXtXmO4/j2oPbwFwtEJNJngM42aJ8sn2S7p149PRTe4SFjJ6TQp9fHz0eTohUpi+PYglB9IeUOIYFc60XQtpHqyd8ulaCUfGew7jlGMN5vWoy//qSJFWkTZ7e3sAwsPD8fX1ZdmyZbx48cLAUYnCIL25i4vExfDZgdX0ObMdIxQeWxTBt9UA/qzROtXyWQ5Sg7DQMtLnyUJDQ5k7dy5eXl6MHj2aJUuW8PjxY72df+HChbi4uGBhYYG7uzsHDx7U27mF4W0PvJdmQmiiTmTIsT/Y/dNQmgefIc7YlFnNetPh47mclIRQpCIqKopevXpRsmRJypYty9y5c9FoNEyaNImKFSty7Ngxli9fnutxSLsmkuYuTpEQKgrtrhxm97Ih9D2zDSMU1tdoReuBi/mzZptkCaGdtSkDmjizdmAjDn3ZShLCQkpvdwoXLlzI6NGjiY+Px9bWFkVRiI6OZvTo0SxbtoyePXuiKAoBAQGplnd4XevWrcPb25uFCxfSpEkTlixZQvv27QkKCqJChQo5fj6Rt6g1Cl/9dSHVba/W5jrsVIsJHsN0tbkGNnORhFCkMH78eA4cOEDfvn3x9/dn1KhR+Pv7Exsby44dO2jevHmuxyDtmkhr7uKy0Q/4etci2tw4CcDN4mWZ4DmMo061k+1na2nCwl7uNKpYQh4VC/3Mfbxt2zY6deqEt7c3Y8aMoUwZ7RVIWFgY3377LfPnz+fvv/9m4cKFVK1alUmTJuV4DA0bNqRevXosWrRIt65atWp07tyZ6dOnZ/h6mSM0fzt8PYJey44nW5dRbS6AAU2dmfg/6UOY1xni++nk5MRPP/1EmzZtuHnzJq6urowYMYI5c+bo5fwg7ZpIOXexsUbNx6f+YvShX7BKiCPeyIRFjd5jYeP3iTMxS/H6xb3ryV3BPKrAzn08c+ZMxo4dy7Rp05KtL1OmDN9//z1WVla0bdsWBweHTDVkWRUfH8/p06cZO3ZssvUeHh4cOXIkx88n8hb/C2GMWPvSTCWKwjuXD+GzdymlYrTdF36v2Qa/lv11tbkA3qnpIAmhSNO9e/d0dQgrVqyIhYUFn3zyid7OL+1a4ZQ0svjB01jsrc35+dh/o4trhV1luv98qj/QThl7vHx1xnt6ccPeMcVxjFQwv6ckhCI5vSSFZ8+eZenSpWlu79OnD35+fuzfvz9XHnlERESgVqspXbp0svWlS5cmPDw81dfExcURFxenW46Ojs7xuETuS+prkyS12lwTPIdyrEKtZK+ztTRhbs96eo1V5C8ajQZT0/9KeBgbG2Ntba2380u7VvikNXexddxzPjv4Mx+d2YaxoiHKwga/Fv35o1YbFFXqQwfm96xLh1qSEIrk9JIUvtp4vsrU1BRLS8tc7wOjemWUlaIoKdYlmT59OlOmTMnVeETuUmsUvlwfCGgHkvQ/9RejDv2qq821qFF3FjZ6P1ltriTfdKsl/WtEuhRFoV+/fpibmwMQGxvL4MGDUySGGzZsyNU4pF0rHNKau9jj6lGm7F5MmWePANjo1oJprT7hkXWxVI9TRkYWi3ToJSmsXr06f/31F6NGjUp1+6ZNm6hePfce09nb22NsbJzi6vnBgwcprrKTjBs3jtGjR+uWo6OjcXRMeQte5E1qjcIXf57jyYtE6ty7gt/O+bg90I48PuZYg/GeXilqc4E0mCLz+vbtm2y5d+/eej2/tGuFR2pzF5eJfsiUPUvwuKbtT3i7mANfeQzloEvKJxw25sZ8UN+RNm4ONHCxkwtekSa9JIVDhw5lyJAhmJubM2jQIExMtKdNTExkyZIlfPXVV7k6o4mZmRnu7u7s3r2bLl266Nbv3r2bTp06pfoac3Nz3R0Akb9sDwzj8z/PYfQ0mimv1Obya9mfP14pxZBk4jvV6NdEpnQSmWPoudqlXSs8Xp672Eij5qMz2/js4M/YxL8gwciYpQ26MvetHsSZpvxsZe5ikRV6SQr79u3L+fPn8fLyYty4cVSqVAmAGzdu8OzZM0aMGEG/fv1yNYbRo0fTp08f6tevT+PGjVm6dCkhISEMHjw4V88r9Gv69iCW7L9Ju6tHmLxnCQ7PIgFYX70lvq0+IdLKNtXXlbA2k4RQ5DvSrhV8L89dXD38OtN3zqdW+HUATpWrxnjPYVwt6Zzm62XuYpEVeqtTOGvWLN577z3Wrl3LtWvaP/BmzZrRs2dPGjVqlOvn/+CDD3j06BFff/01YWFh1KhRg+3bt+Pk5JTr5xb6sT3wHlu2HufH3Ytpe/0EkHZtrldN7VRDGk6R70i7VnAlzc8+d+81rOJfMPrgGj4+vQVjRUO0uTXTW3zMb7U90hxIAtruMDJ3scgKvdQpLAiknlfepo5PYM67Xgz+ezXWCbHEG5mwuGE3Frz1Qaq1uV726dsujOvgpqdIRW6Q72f2yPuWtySVm9kdFM7vp+7yLC6R1teP8/WuxZR7+hCALVWb8XXrQTy0KZ7usVTAIqlBmK8V2DqFQuQm9YmTPO79MWOuXQTgRHk3xnt6cd0+49Hs82X6OiFEHvBquZnSTyP4ds9S2l/V1pwMsS3NRI+h7K/onuGxiluZMr1rTUkIRZZJUijyr6dPuTVkFI6/rsD+39pc01t8zO+12qb7SCXJwg/r0qGWJIRCCMN6udyMkUZNr4AdfLF/FUXiX5CoMuLHBl35oUkPYk0t0j1OMUtTPm7ijFerytIdRmSLJIUif9q0iReDh+J8P0y76Nacqa0Gplmb62VJlfylcKvIrs2bN2d633fffTcXIxH5XdLcxQrgdv8mfjvnUyfsKgBny7zBuHZeXC7lkubri1uZMqljdRyKWki5GfHaJCkU+cudOzBiBGzahCXp1+ZKi1TyF6+rc+fOyZZVKhUvd89+uXi0Wq3WV1giHzoRHEnUwyjGHf6VASc3YaJoiDazYmbzvvxapx0aI+N0Xy+PiUVOyvgZWw5LTExkz549LFmyhKdPnwLaOUSfPXum71BEfqJWww8/gJsbbNqE2tiYBY2649F/QaYTQnMTIxb3riePjMVr02g0un+7du2iTp067Nixg6ioKJ48ecL27dupV68e/v7+hg5V5GFqjcLpRWvY/dNQPj2xARNFw9Y3mtLmk0WsqfdOugmhkQoWfigDSUTO0uudwtu3b9OuXTtCQkKIi4ujbdu2FClShJkzZxIbG8vixYv1GY7IL86cgUGD4PS/8xVXrsWQZoPSrc2VmuV936RJZftcCFAUZt7e3ixevJimTZvq1nl6emJlZcWgQYO4dOmSAaMTeU3SCOOjh87jNnMSXkEHAbhbtCQTPYayr9KbmTqOPPEQuUGvSeHIkSOpX78+586do0SJErr1Xbp04ZNPPtFnKCI/ePYMJk3S3iHUaEgoUpQZzfuy3C1zA0leVsLajEaVSmS8oxBZdOPGDWxtUxZFt7W15datW/oPSORJao3C/L+vs/LgDToc28KX+1dRNC6GRJURy+t3YnbTXrwwS38gCcjIYpG79JoUHjp0iMOHD2NmlrxunJOTE6GhofoMReR1W7fCsGEQEgJAWLt3ebdS9wxrc6VFilOL3PLmm2/i7e3NmjVrKFNG+x91eHg4Y8aMoUGDBgaOTuQF/hfCGLvhPKVvX2OZ/3zc710G4JxDZca38+Ji6UoZHkNGFgt90GtSqNFoUu10fffuXYoUKaLPUEReFRoKI0fC+vXaZWdn1PMX0P60CVHPE7J1yE/fdpHHLCLXLF++nC5duuDk5ESFCtramCEhIVSpUoVNmzYZNjhhcNsDwxi96ggjjvzGwBMbMdWoeWZmybdvf8TPdTtkOJCkeRV7Bjd3lZHFQi/0mhS2bduWOXPmsHTpUkA7Qu/Zs2f4+PjQoUMHfYYi8hq1GhYtgvHj4elTMDaG0aNRT5xEr7XniXoemeVD2lmbMq1TDRlYInKVq6srgYGB7N69m8uXL6MoCm5ubrRp0ybZKGRR+GwPvMc632Xs2rmQCk/uA7CzciN82gwmvGjm+jcPbu5KY+n6IvREr9Pc3bt3j5YtW2JsbMy1a9eoX78+165dw97engMHDlCqVCl9hZJlMh1ULjp3Dj79FI4f1y43bIh68RLmPbRk0T/XiVNn/U/Uu3VlhreWxyyFRV75fsbGxmJubp5vksG88r4VRHv2BRIzbASdLu0H4F4Re3zaDmZ35UaZPkYZWwsOfdlK2rFCqsBPc1e2bFkCAgJYu3YtZ86cQaPRMGDAAHr16oWlpaU+QxF5QUwMTJkC33+vvVNYtCj4+eHftBOj11/geXz26rsNbOaCd9sqORysEKnTaDT4+vqyePFi7t+/z9WrV6lYsSITJ07E2dmZAQMGGDpEoSdqjcKJGxE8/GEBzZfNwjYuBrXKiJXuHfm+aS9izK0yfSwV4NPRTRJCoVd6L15taWlJ//796d+/v75PLfKSHTtg6FBIGp3ZrRvMnYt/pIrBa85k+7ADmzkz4R23nIlRiEyYNm0aq1atYubMmQwcOFC3vmbNmsyePVuSwkLC/0IYq5dtZ9Sf3/NuaBAA50tXYly74VxwcM3SsWSEsTCUXE8KZTookUxYGHh7w++/a5crVIAFC+B//0OtUfjyx13ZOqyFqRHfd68t/QeF3q1evZqlS5fSunVrBg8erFtfq1YtLl++bMDIhL74n7jJNe/xrDy+HjNNIjGmFnzfrDcr3TuizmAgyctkhLEwtFxPCl+dDiotKpVKpoMqyDQaWLoUxo6FJ0+0A0m8vWHyZLCxQa1R+OLPczx5kZjlQ1uYGhHo44mZid4n6BGC0NBQXF1T3gnSaDQkJGRvxLzIP44v/Y2qX46mXZR2Hvbdrg3waTuYe0Uz10fextyYD+o70sbNQUYYC4PL9aRQo9Hk9ilEXnf+vHYgydGj2uX69bUJYt26gPaxy5frA7OVEAJ8372OJITCYKpXr87BgwdxcnJKtv6PP/6g7r9/46IAevCA0AFDabhVWz4r3MYOnzaD2VmlMWRioJEKGCkD4kQeo/c+haIQef4cpk6FWbMgMRFsbMDPT9uX0NgYtUZh3t5rzNl7LdunkBqEwtB8fHzo06cPoaGhaDQaNmzYwJUrV1i9ejVbt241dHgipykKmp+Wo/78c8pFPUaDitX13mHW2x/xLAsDSRZ8WFe6u4g8R+9J4d69e5k9ezaXLl1CpVJRtWpVvL29adOmjb5DEblp505t8nfzpna5SxeYOxd12XIcu/GINcdv8felB9kqNwPaRy4zu9WSRlUYXMeOHVm3bh1+fn6oVComTZpEvXr12LJlC23btjV0eCKHqDUKgXuOYzd6OE4XT2EEXCxVkfGewzhX9o1MH8dIBfN71pOLWZEn6TUpnD9/PqNGjeK9995j5MiRABw7dowOHTrw/fff4+Xlpc9wRG64fx9GjYK1a7XL5cvD/PnQqZN2qqflu7M9M0mSjrUcmNOjnjxyEQaXmJiIr68v/fv3Z//+/YYOR+QCtUZhkf9FTGfO4OOD6zDTJPLc1Jzvm/ZiRf1OWRpIAjC/Z11JCEWepdfi1eXKlWPcuHEpkr8FCxbg6+vLvXv39BVKlkmR1wxoNPDTT/DFFxAVBUZGMGIEfP01amub135MnGR+j7r8r47cHRTJGfL7aWNjw4ULF3B2dtbreXOCtGvp878Qxp/f/cy4zXOpFBkKwN8V6zPJYwh3bUtn6VhlbC3w6egmZWZEphX44tXR0dG0a9cuxXoPDw++/PJLfYYiclJQkHYgyaFD2uW6deHHH8Hd/d9BJEeyPYjkZQulD47Ig9q0acM///xDv379DB2KyEG791/gmZc3yy7sBeCBdXEmt/mU7W80ydRAEtAOJun3ljMe1WVkscgf9JoUvvvuu2zcuJHPP/882fq//vqLjh076jMUkRNevABfX5g5ExISwNoapk0DLy8wMWF7YBhDf81+Ieok0gdH5GXt27dn3LhxXLhwAXd3d6ytrZNtl/qr+YyicM73B9z9fLB7EY0GFWvqduDb5h/x1Nw649e/RAaTiPxGr0lhtWrV8PX15Z9//qFx48aAtk/h4cOHGTNmDHPnztXtO2LECH2GJrJq714YPBiuX9cud+yo7TtYoQIAWwPu4fXb2Rw5lfTBEXnZkCFDAPj+++9TbJP6q/nM1as86tOf2icOA3CppDPjPb04W65qlg81qk0VSQhFvqPXPoUuLi6Z2k+lUnEzadRqHiF9b/718CGMHg1r1miXy5ZF/cNcjtV6m6PBj9AocOb2Y44FR772qWSqJ5FZ8v3MHnnftNQvYrk3bjJlF87GOCGeFybm/NCkJ8ve7EyicdbvnTgUNefw2NbyuFi8lgLfpzA4OFifpxM56aXaXKZRj1FUKm5078uK9gPYGPiM56dO5OjpvFu7Mrx1FWlURb4SGxuLhYWFocMQWXB85UZKf+GN88MQAPa71OMrj6HcKeaQreOpgMnvVpe2S+RLUrxaZEgddImwnv0oH3gCIyColAvjPL20tbkuP8nRc8ndQZHfqNVq/Pz8WLx4Mffv3+fq1atUrFiRiRMn4uzszIABAwwdokhNZCR3BnrRcIO2fNZD62JMbTWQzdXezvRAklfJCGOR3+k1KVQUhT///JN9+/bx4MGDFFPgbdiwQZ/hiHSoNQonL98jbqovjf9YRnl1As9NzZndpBfL38x6ba70WJgY0bJqKXo3cqJRxRJyhS3yFV9fX1atWsXMmTMZOHCgbn3NmjWZPXu2JIV5jaKg+XkNiaNG4xgZAcCvtdsxo0U/oi1sMn0YG3NjuruXp3xxK+xszHEoaiEjjEW+p9ekcOTIkSxdupSWLVtSunRpVNm8GhO5R61RmP/3dc6v2ci4Lf/V5tpX0Z2JHkOzXJsrI/KYWOR3q1evZunSpbRu3ZrBgwfr1teqVYvLly8bMDIB2jbtRHAkD57GUj4iFPsvRuF09ghmwNUSFRjXzovT5d0yfTyZs1gUZHpNCtesWcOGDRvo0KGDPk8rMsn/Qhgzfj7EsO1LGXlhD5C92lyZIY+JRUERGhqKq6trivUajYaEhNebvUe8Hv8LYUzZEkRE5FMGntiI55HfsEiMJ9bEjLlv9eDHBl1IMDbN0jGlzIwoyPSaFNra2lKxYkV9nlKk4+Ur6OAHzwiZu4QNf/+kq831S932fPv2R1l6pJIZI1q6MrKt3B0UBUP16tU5ePAgTk5Oydb/8ccf1K1b10BRCf8LYQxZc4Z6d4NYuXM+b0RoB5IcdKrDV55DuV0864mdlJkRBZ1ek8LJkyczZcoUli9fjqWlpT5PXai9nPzZW5uDCvZeus+mgHtExsTjHBmK764FeN8OBLS1uSZ4DuNMuWo5Hsunb7sw2jPzk8cLkdf5+PjQp08fQkND0Wg0bNiwgStXrrB69Wq2bt1q6PAKHbVG4diNR0xbcwRf/2V8eM4fgAgrW6a2+oS/3Fpk66mHQ1FzvFqlvCMsREGi16Swe/furF27llKlSuHs7IypafLb9mfOvP7sF0IrKRHcHRSuS/5eZZaYgNeJ9Qw/sg5zdQIvTMyZ26QHP77ZJVu1udJjY27MzG615CpbFDgdO3Zk3bp1+Pn5oVKpmDRpEvXq1WPLli20bdvW0OEVKv4Xwpiy+SL1j+1i498/UjImCoDfankwvcXHPLEskuVjJqWPUmZGFAZ6TQr79evH6dOn6d27tww0yWEv3w28FfGctSdCCI+OTXP/Bncu4LtzAZUf3QHggHNdJngOy3ZtrrQUszTl4ybOeLWSTtmi4PL09MTT09PQYRRq/hfC8Ju/nRm7FtI8WHuD4bpdeca38+KEY41sH9dBysyIQkSvSeG2bdvYuXMnTZs21edpC7ykztRhT9JOApPYvnjKuH9W0CNwFwAPrYoxtfXr1eZKYm1mTLPK9rg72WFfREo0CCH0Qx0Xz43PJrFz789YJsYRZ2zK/Mbvs6The8SbZG0gCWgHwk3qWF3aMFHo6DUpdHR0NMhUSr6+vmzbto2AgADMzMyIiorSewyv4+W7gKWKaBspQPd4ePnhWxkfRFHoHPQPX/29DPvn2oLT2anNBWBrYUJbt9I0rmRP1PN4qdElCp3ixYtn+klHZOTrT/koUqfWKARt2EXx0V4Mu6Odh/1IhVpM8BxGsF25bB1TBVIZQRRaek0Kv/vuO7744gsWL16Ms7Oz3s4bHx9P9+7dady4MT/99JPezpsTUrsLWMxKe+Ub9Txz5S6cHt9j2s6FNLsdAGSvNpeNuTEf1HekjZuDJH+i0JszZ47u50ePHjFt2jQ8PT1p3LgxAEePHmXnzp1MnDjRQBEWTEkXyOFPXnA6MJiaC2bS/dQ2jFCItCzKtFYD2FC9lcxIIkQ2qRRFUfR1suLFi/P8+XMSExOxsrJKMdAkt6+oV65cibe3d7buFOb2xNSp3Q3cHRTOkDVnyO4HZKpOYNDxDYw48hvm6gTijE35oUnPLNXmkkKtIj8wxMTxSbp160bLli3x8vJKtn7+/Pns2bOHTZs26TWerDDk+5YVSUX1VxwOJup5PB2uHGbyniWUinkMwJ81WuPbsj+PrWyzdNykpx5NKpeUpx0izzHE91OvdwpfvrrO6+Li4oiLi9MtR0dH635OLYHLqCFJ7zWp3Q10KGpObKIm2wmh+90g/HKgNpcUahUifTt37uSbb75Jsd7T05OxY8caIKL86eW7gJEx8RSzMiPqeTx3o17wx6m7PItLpPyT+3y3ezGtb5wE4IZdOb7yGMZRp1qZPo/0FxQibXpNCvv27avP072W6dOnM2XKlBTrdweFM2vfyWQJXEaPHFJL+pJeA6R6NzA8Oo7sKBr7jLH/rHzt2lzyGEWIzClRogQbN27k888/T7Z+06ZNlChRwkBR5R/J7gK+SL1LjLFGzcCTfzHq8C9YJcQRZ2zCokbdWdSoO3EmZpk+l/QXFCJ9ek0KX/bixYsUU0Bl5fZoUiHs9Jw8eZL69etnK75x48YxevRo3XJ0dDSOjo6MXncOlblVsn3Dn8QyZM0ZFvWul6KxSaqqnyLpexLL4DVnKGZlmu27gckoCh0vHWDSK7W5ZrToR5Rl2u+rnbUpXeqUo1XV0qCCiGdxmb77KYSAKVOmMGDAAP755x9dn8Jjx47h7+/PsmXLDBxd3vRyHdXf/70LmJba964wfed83B4EA3DMsQYTPIdxo4Rjls4pF7pCZEyvSWFMTAxffvklv//+O48ePUqxXa1WZ/pYXl5e9OjRI919Xmcwi7m5Oebm5inWK/xXzPTVdVO2BNHWzUGXTKk1ClO2BKWa9CWty+xgkfQ4RoUzLYPaXJL8CZE7+vXrR7Vq1Zg7dy4bNmxAURTc3Nw4fPgwDRs2NHR4eU5mS2jZxD3nswOr+eiMdiDJY4si+LX8mD9qts3SUw9bSxMW9nKnUcUS0tYJkQG9JoVffPEF+/btY+HChXz00UcsWLCA0NBQlixZwowZM7J0LHt7e+zt7XMp0qxTgLAnsZwIjqRxJe0joxPBkZmqHZhdJupEPjm5iZGH1/5bm8uEBY0/YHHD97Czs2FUgwo421tL8idELklISGDQoEFMnDiRX375xdDh5HnbA8MY+msGM1cpCp5XjzJlz2IcnmkHH66v3hLfVp8QmYWBJEmt3TfdatHENe/8XyFEXqbXpHDLli2sXr2aFi1a0L9/f5o1a4arqytOTk788ssv9OrVK1fOGxISQmRkJCEhIajVagICAgBwdXXFxiZrNfoy8uBpbKo/57S6oZfx2zmfag9vAf/V5mrVsQmrpGyMEHphamrKxo0bpfRMJmwPvIfX2rPp7lM2+gFTdi+h7fXjAAQXL8NXHsM47Fwny+eTmUiEyDq9JoWRkZG4uLgA2v6DSSVomjZtypAhQ3LtvJMmTWLVqlW65bp16wKwb98+WrRokaPnKlXEItWfs0MF2FqZYmFirJuyrkhcDBMP/8x7p7ZhpGhrc/m2HMCRJh3webe6NIBC6FmXLl3YtGlTsj7IIjntHcK0E0JjjZq+p7cy5uDPWCfEEm9kwpKG3Zjf+H3iTFN240mL1FMV4vXoNSmsWLEit27dwsnJCTc3N37//XcaNGjAli1bKFasWK6dd+XKlaxcuTJHjpVWE6NCe2WaNNsIQAMXO8rYWhD+JDbVfoVJSd+Tf/sVKq9sA5jRtSZt3Rw4cfMRJhvXU/vbSZg9fADAg249OT1sHO9VKMtMaQCFMAhXV1emTp3KkSNHcHd3x9raOtn2ESNGGCgyw1NrFObuvcbcvdfS3KdG+HWm+8+j5v0bAJws58Z4z2FcK+mU6fPIHOtC5Ay9Fq+ePXs2xsbGjBgxgn379vHOO++gVqtJTEzk+++/Z+TIkfoKJcuSikhW8P4dI3OrVBO49EYfQ+pJ36Le9QDSLFnTrkYZuHULvLxg2zbtxsqVYckSaNkyx34/IfIzQxZhTnr6kRqVSsXNmzf1GE3W5OT79mqdwZfrC6bGOu45Yw6uoe+ZrRgrGp6YWzO9xcesq+2BojJK91xSdFoUBoZo1/SaFL7q9u3bnD59mkqVKlG7dm1DhZEpSR/On0evMGvfnRyrU5j0mlSLW2vUMGcO+PjA8+dgagrjxmn/Wbzeo2khCpL8MjNHXpMT71tm6gy+qu21Y0zZvZiyTyMA2OTWnGmtPiHCuniar0mqoCCPhkVhUeiSwvzk5Q/H2qZIjs5okqoTJ2DQIDh3TrvcrJn27mC1ajn4WwlRMOSFpDAiIgKVSpWvCla/zvuWlAwuOXCD5/GZKyfmEB3B5L1LaHf1KAAhtqX5ymMoByq66/ZJugvYuJI9Uc/jsbMxl7uBolAqsNPcHT9+nMjISNq3b69bt3r1anx8fIiJiaFz587Mmzcv1bqAeZGxkUpXdibHXxMdDV99BfPng6JA8eIwaxb06wdG6T9SEULoV1RUFBMmTGDdunU8fqydh7d48eL06NGDadOm5WpfaUPyvxDG2A3nM11n1Uijps/Z7Xx2YDVF4l+QYGTMjw26MPetHsSaWqAC+r3ljEd1uQsohCHpJSmcPHkyLVq00CWF58+fZ8CAAbqir99++y1ly5Zl8uTJ+ggnb1IU2LgRhg+He/e063r3hu++g1KlDBubECKFyMhIGjduTGhoKL169aJatWooisKlS5dYuXIle/fu5ciRIxQvnvYj0fzI/0IYg9dkUGvwJW73b+K3cx51wrSDTc6UfYPxnl5cLvVfX0yZY12IvEEvSWFAQABTp07VLf/22280bNiQH3/8EQBHR0d8fHwKb1IYEqIdSLJli3a5UiVYvBjatDFsXEKINH399deYmZlx48YNSpcunWKbh4cHX3/9NbNnz86V8/v6+rJt2zYCAgIwMzMjKioqV87zsvhEDeM3XsjUvlbxL/A+9Cv9T/2FiaIh2tyamc378kuddrqBJEYqmN+zHh1qSSktIfICvTyPfPz4cbJGc//+/bRr1063/Oabb3Lnzh19hJK3JCbC7Nng5qZNCE1MYPx4OH9eEkIh8rhNmzYxa9asFAkhgIODAzNnzmTjxo25dv74+Hi6d++eqzVek6g1Cj/suUbdr3cRGROf4f6trp9g109DGXRyIyaKhq1Vm9H6k0Wsqdsh2cji+T3rSkIoRB6ilzuFpUuXJjg4GEdHR+Lj4zlz5gxTpkzRbX/69Cmmpqb6CCXvOH1aO5DkzL+PYZo00Q4kqV7dsHEJITIlLCyM6ul8X2vUqEF4eHiunT+pDc2pGqxpyUr/wVJPH+GzdynvXDkMwN2ipfjKYwj/VHoz2X7FrUyZ3rWmFNsXIo/RS1LYrl07xo4dyzfffMOmTZuwsrKiWbNmuu2BgYFUqlRJH6EY3tOnMGkSzJ0LGg0UKwYzZ8KAATKQRIh8xN7enlu3blG+fPlUtwcHB+e5kchxcXHExcXplqOjo9PdP7P9B400aj4M8OeL/asoGv+cRJURP73ZmTlNPuSF2X/ls6TItBB5m16SwmnTptG1a1eaN2+OjY0Nq1atwszMTLd9+fLleHh46CMUw/rrL23fwbt3tcs9e2ofH6fy+EkIkbe1a9eOCRMmsHv37mTtGWiTr4kTJybrJpMXTJ8+PdlTmrSoNQrHbjziy/XnM9y36oNg/HbOp969KwAElKnCeE8vgkpXBKS+oBD5iV7rFD558gQbGxuMjY2TrY+MjMTGxiZFw5qXvFa9oLt3taOKN23SLru4wKJF4OmZ43EKURgZop7X3bt3qV+/Pubm5gwbNoyqVasCEBQUxMKFC4mLi+PUqVM4Ojpm+piTJ0/OMGk7efIk9evX1y2vXLkSb2/vTA00Se1OoaOjY7L6q7uDwtkUcC/DvoOW8bGMPLKWT05o+w0+NbPk27c/YkOD/9GudnmZbUSI11Rg6xQmsbW1TXW9nZ1dquvzPbUaFi6ECRO0j41NTGDMGO3jYysrQ0cnhHgN5cuX5+jRowwdOpRx48aRdH2tUqlo27Yt8+fPz1JCCODl5UWPHj3S3cfZ2Tm7IWNubp5qPdjdQeHM2ncy2axL6Wl+8zTTdi3E8cl9ALZXeYtZHYbQ6Z0GnJNHw0LkW3pNCguVgADtQJKTJ7XLjRrB0qVQs6ZBwxJC5BwXFxd27NjB48ePuXZNW4fP1dU12xe69vb22Nvb52SImTJ63TlU5hlfqJZ89phJe5fS8fJBAEKLlMSn7WDO1GnKsXFtMDORftFC5GeSFOa0mBjtXMVz5mjvFBYtCjNmwKefykASIQqo4sWL06BBA72eMyQkhMjISEJCQlCr1QQEBADapNTGxiZLx1KA9O7tqRQNPc7tYuw/K7CNi0GtMmJ5/XeZ3bQXL8wsWdSlpiSEQhQAkhTmpG3bYOhQbTFqgPff1yaHZaTsghAiZ02aNIlVq1bpluvWrQvAvn37aNGiRY6dp8rDW/jtXED90EsABDq4Ms7Ti4sOrhS3MuV7KS0jRIEhSWFOuHcPRo6EP//ULjs5afsSduhg2LiEEAXWypUrc7VGoXlCHCOO/MagExsw1ah5ZmbJd816s6re/9AYGfNevfJ8814t6T8oRAEiSeHr0Gi009GNGwfR0WBsDKNGweTJYG1t6OiEECJbmgafxXfXApyitMW3d1VuhE+bTwkrWhIAh6LmkhAKUQBJUphdgYHafoLHjmmX33xTO5CkTh2DhiWEEFmVlNqViIli4t8/0jloPwD3itgzuc2n7KrSONm+k9+tLgmhEAWQJIXZERQE7u7auYuLFAE/PxgyRHunUAgh8iHzxAS2rhxJmWePUKuMWFXvf3zXrDcxL41KLmNrgU9HN+lDKEQBJUlhdlSrBu3bg6mpdrq6cuUMHZEQQmTb9x/UZta+O6xy78j/Lh9knKcXoa5uvF+7LOWLW2FnYy6FqIUoBCQpzA6VCn7/HSwsMt5XCCHyuLZuDnRuUJkTXWtw82ks44vbSAIoRCEkSWF2SUIohChAjI1UNH5D5mEXojCTaqNCCCGEEEKSQiGEEEIIIUmhEEIIIYRA+hRmmqIoAERHRxs4EiHEq5K+l0nfU5E50q4JkXcZol2TpDCTnj59CoCjo6OBIxFCpOXp06fY2toaOox8Q9o1IfI+fbZrKkUurTNFo9Fw7949ihQpgkr1+mUaoqOjcXR05M6dOxQtWjQHItQvid+wJP7kFEXh6dOnlC1bFiMj6RWTWa+2a/n97yoj8vvlb4Xt9zNEuyZ3CjPJyMiI8uXL5/hxixYtmq//uCV+w5L4/yN3CLMurXYtv/9dZUR+v/ytMP1++m7X5JJaCCGEEEJIUiiEEEIIISQpNBhzc3N8fHwwNzc3dCjZIvEblsQvckNB/1zk98vf5PfLfTLQRAghhBBCyJ1CIYQQQgghSaEQQgghhECSQiGEEEIIgSSFBnfr1i0GDBiAi4sLlpaWVKpUCR8fH+Lj4w0dWqb5+vry1ltvYWVlRbFixQwdToYWLlyIi4sLFhYWuLu7c/DgQUOHlGkHDhygY8eOlC1bFpVKxaZNmwwdUqZNnz6dN998kyJFilCqVCk6d+7MlStXDB2W+FdmvschISF07NgRa2tr7O3tGTFiRL5qq17m7OyMSqVK9m/s2LGGDivb8nO7lp7Jkyen+JwcHBwMHVa2ZdSGK4rC5MmTKVu2LJaWlrRo0YKLFy/qLT5JCg3s8uXLaDQalixZwsWLF5k9ezaLFy9m/Pjxhg4t0+Lj4+nevTtDhgwxdCgZWrduHd7e3kyYMIGzZ8/SrFkz2rdvT0hIiKFDy5SYmBhq167N/PnzDR1Klu3fv59hw4Zx7Ngxdu/eTWJiIh4eHsTExBg6NEHG32O1Ws0777xDTEwMhw4d4rfffmP9+vWMGTNGz5HmnK+//pqwsDDdv6+++srQIWVLfm/XMlK9evVkn9P58+cNHVK2ZdSGz5w5k++//5758+dz8uRJHBwcaNu2rW5KylyniDxn5syZiouLi6HDyLIVK1Yotra2hg4jXQ0aNFAGDx6cbF3VqlWVsWPHGiii7AOUjRs3GjqMbHvw4IECKPv37zd0KOIlaX2Pt2/frhgZGSmhoaG6dWvXrlXMzc2VJ0+e6DHCnOHk5KTMnj3b0GHkiILUrr3Kx8dHqV27tqHDyBWvtuEajUZxcHBQZsyYoVsXGxur2NraKosXL9ZLTHKnMA968uQJdnZ2hg6jwImPj+f06dN4eHgkW+/h4cGRI0cMFFXh9eTJEwD5W88njh49So0aNShbtqxunaenJ3FxcZw+fdqAkWXfN998Q4kSJahTpw6+vr758lF4YWjXrl27RtmyZXFxcaFHjx7cvHnT0CHliuDgYMLDw5N9lubm5jRv3lxvn6XMfZzH3Lhxg3nz5vHdd98ZOpQCJyIiArVaTenSpZOtL126NOHh4QaKqnBSFIXRo0fTtGlTatSoYehwRCaEh4en+O4UL14cMzOzfPn9GTlyJPXq1aN48eKcOHGCcePGERwczLJlywwdWpYU9HatYcOGrF69mipVqnD//n2mTZvGW2+9xcWLFylRooShw8tRSZ9Xap/l7du39RKD3CnMJal1jn3136lTp5K95t69e7Rr147u3bvzySefGChyrezEn1+oVKpky4qipFgncpeXlxeBgYGsXbvW0KEUaDn9PU7te5KXvj9Z+X1HjRpF8+bNqVWrFp988gmLFy/mp59+4tGjRwb+LbKnoLZr7du3p1u3btSsWZM2bdqwbds2AFatWmXgyHKPIT9LuVOYS7y8vOjRo0e6+zg7O+t+vnfvHi1btqRx48YsXbo0l6PLWFbjzw/s7e0xNjZOcfX84MGDFFdmIvcMHz6czZs3c+DAAcqXL2/ocAq0nPweOzg4cPz48WTrHj9+TEJCQp75/rzO79uoUSMArl+/nq/uQBW2ds3a2pqaNWty7do1Q4eS45JGVYeHh1OmTBnden1+lpIU5hJ7e3vs7e0ztW9oaCgtW7bE3d2dFStWYGRk+Bu4WYk/vzAzM8Pd3Z3du3fTpUsX3frdu3fTqVMnA0ZWOCiKwvDhw9m4cSP//PMPLi4uhg6pwMvJ73Hjxo3x9fUlLCxM9x/Wrl27MDc3x93dPUfO8bpe5/c9e/YsQLL/jPODwtauxcXFcenSJZo1a2boUHKci4sLDg4O7N69m7p16wLaPqP79+/nm2++0UsMkhQa2L1792jRogUVKlRg1qxZPHz4ULctv9RiCgkJITIykpCQENRqNQEBAQC4urpiY2Nj2OBeMXr0aPr06UP9+vV1d2VDQkIYPHiwoUPLlGfPnnH9+nXdcnBwMAEBAdjZ2VGhQgUDRpaxYcOG8euvv/LXX39RpEgR3Z0NW1tbLC0tDRydyOh77OHhgZubG3369OHbb78lMjKSzz77jIEDB1K0aFHDBp9FR48e5dixY7Rs2RJbW1tOnjzJqFGjePfdd/P89yg1+b1dS89nn31Gx44dqVChAg8ePGDatGlER0fTt29fQ4eWLRm14d7e3vj5+VG5cmUqV66Mn58fVlZWfPjhh/oJUC9jnEWaVqxYoQCp/ssv+vbtm2r8+/btM3RoqVqwYIHi5OSkmJmZKfXq1ctXJVH27duX6nvdt29fQ4eWobT+zlesWGHo0ISSue/x7du3lXfeeUextLRU7OzsFC8vLyU2NtZwQWfT6dOnlYYNGyq2traKhYWF8sYbbyg+Pj5KTEyMoUPLtvzcrqXngw8+UMqUKaOYmpoqZcuWVbp27apcvHjR0GFlW0ZtuEajUXx8fBQHBwfF3Nxcefvtt5Xz58/rLT6VoihK7qeeQgghhBAiLzN85zUhhBBCCGFwkhQKIYQQQghJCoUQQgghhCSFQgghhBACSQqFEEIIIQSSFAohhBBCCCQpFEIIIYQQSFIohBBCCCGQpLDQunXrFiqVSjeVVX7h7OzMnDlzcux4LVq0wNvbO8eOZ0gqlYpNmzYB+ffzFeJ15Ne/e2nX0ibtmn5JUlgAqVSqdP/169fP0CFmaOXKlRQrVizF+pMnTzJo0CC9xvLixQt8fHx44403MDc3x97envfee4+LFy/qNY4kkydPpk6dOinWh4WF0b59e/0HJIQeSLuWs6RdE6kxMXQAIueFhYXpfl63bh2TJk3iypUrunWWlpY8fvzYEKGhVqtRqVQYGWXveqRkyZI5HFH64uLiaNOmDSEhIXz33Xc0bNiQ+/fvM336dBo2bMiePXto1KiRXmNKi4ODg6FDECLXSLuWc6RdE2nS2yzLwiBWrFih2NraplgfHBysAMr69euVFi1aKJaWlkqtWrWUI0eOJNvv8OHDSrNmzRQLCwulfPnyyvDhw5Vnz57ptkdGRip9+vRRihUrplhaWirt2rVTrl69muL8W7ZsUapVq6YYGxsrN2/eVOLi4pTPP/9cKVu2rGJlZaU0aNBA2bdvn6IoqU8Y7uPjoyiKojg5OSmzZ8/WHf/x48fKwIEDlVKlSinm5uZK9erVlS1btiiKoigRERFKjx49lHLlyimWlpZKjRo1lF9//TXZ79e8eXNl5MiRab5/M2bMUFQqlRIQEJBsvVqtVurXr6+4ubkpGo0mzWN16tRJN9G5oijKzz//rLi7uys2NjZK6dKllZ49eyr379/XbU/63ffs2aO4u7srlpaWSuPGjZXLly/r3s9X35sVK1YoiqIogLJx40ZFUf77fM+ePas79sWLF5X27dsr1tbWSqlSpZTevXsrDx8+1G3/448/lBo1aigWFhaKnZ2d0rp162SftRB5hbRr0q4lkXYtZ8nj40JuwoQJfPbZZwQEBFClShV69uxJYmIiAOfPn8fT05OuXbsSGBjIunXrOHToEF5eXrrX9+vXj1OnTrF582aOHj2Koih06NCBhIQE3T7Pnz9n+vTpLFu2jIsXL1KqVCk+/vhjDh8+zG+//UZgYCDdu3enXbt2XLt2jbfeeos5c+ZQtGhRwsLCCAsL47PPPksRu0ajoX379hw5coQ1a9YQFBTEjBkzMDY2BiA2NhZ3d3e2bt3KhQsXGDRoEH369OH48eOZfn9+/fVX2rZtS+3atZOtNzIyYtSoUQQFBXHu3LlMHy8+Pp6pU6dy7tw5Nm3aRHBwcKqPvSZMmMB3333HqVOnMDExoX///gB88MEHjBkzhurVq+vemw8++CDD84aFhdG8eXPq1KnDqVOn8Pf35/79+7z//vu67T179qR///5cunSJf/75h65du6IoSqZ/NyHyCmnX0iftmrRraTJsTipyW0ZX1MuWLdOtu3jxogIoly5dUhRFUfr06aMMGjQo2esOHjyoGBkZKS9evFCuXr2qAMrhw4d12yMiIhRLS0vl999/150fSHZFev36dUWlUimhoaHJjt26dWtl3Lhx6cb98hX1zp07FSMjI+XKlSuZfj86dOigjBkzRrec0RW1hYVFmtvPnDmjAMq6devSPNarV9SvOnHihAIoT58+VRQl+RV1km3btimA8uLFC0VRFMXHx0epXbt2imORzhX1xIkTFQ8Pj2T737lzRwGUK1euKKdPn1YA5datW2nGKkReIe1actKu/UfatdcjfQoLuVq1aul+LlOmDAAPHjygatWqnD59muvXr/PLL7/o9lEUBY1GQ3BwMNeuXcPExISGDRvqtpcoUYI33niDS5cu6daZmZklO8+ZM2dQFIUqVaokiyUuLo4SJUpkOvaAgADKly+f4jhJ1Go1M2bMYN26dYSGhhIXF0dcXBzW1taZPkd6lH+vNs3MzDL9mrNnzzJ58mQCAgKIjIxEo9EAEBISgpubm26/tD6XChUqZCvW06dPs2/fPmxsbFJsu3HjBh4eHrRu3ZqaNWvi6emJh4cH7733HsWLF8/W+YQwJGnXsk/atcJNksJCztTUVPezSqUC0H2hNRoNn376KSNGjEjxugoVKnD16tVUj6koiu5YoO0A/vKyRqPB2NiY06dP6x6JJEnty50WS0vLdLd/9913zJ49mzlz5lCzZk2sra3x9vYmPj4+0+eoXLkyQUFBqW67fPkygK7xNjIySvFY4uXHTTExMXh4eODh4cGaNWsoWbIkISEheHp6pogpvc8lOzQaDR07duSbb75Jsa1MmTIYGxuze/dujhw5wq5du5g3bx4TJkzg+PHjuLi4ZPu8QhiCtGvpk3ZN2rW0SFIo0lSvXj0uXryIq6trqtvd3NxITEzk+PHjvPXWWwA8evSIq1evUq1atTSPW7duXdRqNQ8ePKBZs2ap7mNmZoZarU43vlq1anH37l2uXr2a6lX1wYMH6dSpE7179wa0Dci1a9fSje1VPXv2ZMKECZw7dy5Z/xuNRsPs2bOpX7++7kq4ZMmSyUZIqtVqLly4QMuWLQFtYxsREcGMGTNwdHQE4NSpU5mOJUlm3ptX1atXj/Xr1+Ps7IyJSepfe5VKRZMmTWjSpAmTJk3CycmJjRs3Mnr06CzHKEReJe2atGvSrqVNBpqINH355ZccPXqUYcOGERAQwLVr19i8eTPDhw8HtFebnTp1YuDAgRw6dIhz587Ru3dvypUrR6dOndI8bpUqVejVqxcfffQRGzZsIDg4mJMnT/LNN9+wfft2QFvM9dmzZ+zdu5eIiAieP3+e4jjNmzfn7bffplu3buzevZvg4GB27NiBv78/AK6urrqrxEuXLvHpp58SHh6epfdg1KhRNGjQgI4dO/LHH38QEhLCyZMn6datG9euXWPlypW6fVu1asW2bdvYtm0bly9fZujQoURFRem2V6hQATMzM+bNm8fNmzfZvHkzU6dOzVI8Se9NcHAwAQEBREREEBcXl+Frhg0bRmRkJD179uTEiRPcvHmTXbt20b9/f9RqNcePH8fPz49Tp04REhLChg0bePjwYZb+oxEiP5B2Tdo1adfSYajOjEI/MuqQ/fLQ/sePHyuAroSComg7DLdt21axsbFRrK2tlVq1aim+vr667UmlG2xtbRVLS0vF09Mz1dINr4qPj1cmTZqkODs7K6ampoqDg4PSpUsXJTAwULfP4MGDlRIlSqRbuuHRo0fKxx9/rJQoUUKxsLBQatSooWzdulW3rVOnToqNjY1SqlQp5auvvlI++ugjpVOnTrrXZ9QhW1EU5dmzZ8qECROUSpUqKSYmJgqguLq6Knfu3EnxOw0ZMkSxs7NTSpUqpUyfPj1Fh+xff/1VcXZ2VszNzZXGjRsrmzdvTvY5JHXIfvz4se41Z8+eVQAlODhYURRFiY2NVbp166YUK1YsS6Ubrl69qnTp0kVXZqNq1aqKt7e3otFolKCgIMXT01MpWbKkYm5urlSpUkWZN29euu+LEIYi7Zq0a0mkXctZKkWRsdlCZMWOHTvo0qULs2bNSlbGQggh8itp1wTI42Mhsqx9+/bs2LGDyMhIIiIiDB2OEEK8NmnXBIDcKRRCCCGEEHKnUAghhBBCSFIohBBCCCGQpFAIIYQQQiBJoRBCCCGEQJJCIYQQQgiBJIVCCCGEEAJJCoUQQgghBJIUCiGEEEIIJCkUQgghhBBIUiiEEEIIIYD/A4iCKvj5vL32AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extended Exercise\n",
    "\n",
    "def visualiseResids(x, y, y_pred):\n",
    "    resids = y-y_pred\n",
    "\n",
    "    # Plot 1\n",
    "    plt.subplot(2, 2, 1)\n",
    "    plt.scatter(y_pred, y)\n",
    "    plt.plot([min(y_pred), max(y_pred)], \n",
    "             [min(y_pred), max(y_pred)], \n",
    "             color='red', linestyle='--', linewidth=2)\n",
    "    plt.xlabel(\"Predicted Values\")\n",
    "    plt.ylabel(\"Actual Values\")\n",
    "    plt.title(\"Predicted vs Actual Values\")\n",
    "    \n",
    "    # Plot 2\n",
    "    plt.subplot(2, 2, 2)\n",
    "    plt.scatter(x, resids)\n",
    "    plt.axhline(y=0, color='red', linestyle='--', linewidth=2)\n",
    "    plt.xlabel(\"X Values\")\n",
    "    plt.ylabel(\"Residuals\")\n",
    "    plt.title(\"Residuals vs X Values\")\n",
    "    \n",
    "    # Plot 3\n",
    "    plt.subplot(2, 2, 3)\n",
    "    qqplot(resids, line='s', ax=plt.gca());\n",
    "    plt.title(\"QQ Plot of Residuals vs Normal Distribution\")\n",
    "    \n",
    "    # Plot 4\n",
    "    plt.subplot(2, 2, 4)\n",
    "    qqplot_2samples(x, resids, line='r', ax=plt.gca());\n",
    "    plt.xlabel(\"Theoretical Quantiles\")\n",
    "    plt.ylabel(\"Ordered Residuals\")\n",
    "    plt.title(\"QQ Plot of Residuals vs X Values\")\n",
    "\n",
    "    plt.tight_layout()\n",
    "    plt.show()\n",
    "\n",
    "# Example\n",
    "X = sm.add_constant(x)\n",
    "model = sm.OLS(y_sin, X)\n",
    "results = model.fit()\n",
    "y_pred = results.predict(X)\n",
    "resids = y_pred - y_sin\n",
    "\n",
    "visualiseResids(x, y_sin, y_pred)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Autocorrelation in Residuals\n",
    "\n",
    "Another issue that can arise is when there is autocorrelation in the residuals. This happens when the data is noisy in the \"macro\" sense, but correlated in the \"micro\" sense.\n",
    "\n",
    "Here is an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generate a dataset\n",
    "# Errors have a autocorrelation with lag 1\n",
    "errors = np.random.randn(len(x)) * 3 + 5\n",
    "# Errors are dependent on the previous error to some degree\n",
    "errors[1:] += 0.5 * errors[:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# y = mx + c + e\n",
    "y_corr = 2 * x + 6 + errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x23c42a7b288>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_corr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fit_linear_plot_residuals(x, y_corr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the above graph, the errors *look* random enough, and it would be hard to actually see any correlation here. Especially with so many data.\n",
    "\n",
    "However, let us extract the residuals and test for autocorrelation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x23c42b16348>"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = sm.add_constant(x)\n",
    "model = sm.OLS(y_corr, X)  # Capital X, which has constants already\n",
    "results = model.fit()\n",
    "y_pred = results.predict(X)\n",
    "\n",
    "e_corr = y_pred - y_corr\n",
    "plt.plot(x, e_corr, 'ro')\n",
    "plt.hlines(0, xmin=x.min(), xmax=x.max())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_acf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Object `autocorrelation_plot` not found.\n"
     ]
    }
   ],
   "source": [
    "autocorrelation_plot??"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(e_corr, lags=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This plot shows a clear autocorrelation in the residuals at lag 1. Other values, such as 11 and 14 show a \"significant\" autocorrelation, but unless you had a significant reason to suspect a cyclic trend of this length (for instance, if your customers are on a 14 week rolling schedule), I would consider this \"unlucky\" in the null-hypothesis-false-positive sense.\n",
    "\n",
    "In this case, the residuals are not white noise and therefore we must examine for other trends in the data we are not accounting for. In this case, revisit some of the models we have seen, such as ARIMA, which is likely to be able to address this problem. In cases of autocorrelation, OLS is unable to adequately address the issue by itself."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.18"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
